For the question, I got answer choice b? Is that correct, because even though I got it correct, I feel like it is wrong. How can I check my answer? PLEASE HELP!

(x+1)^2 - 36 = (x+1)^2 = 36 | *Add 36 to both sides to cancel out. = x+1 = +/-6 | *Take the plus-or-minus square root of both sides, since x could be positive or negative. 36 becomes plus-or-minus 6. If you would like a better understanding of this principle, watch this khan video. It explains it in detail starting at 1: 37. https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/v/simple-quadratic-equation x = either (6-1 = 5) or (-6-1 = -7) | *Subtract 1 from both sides to cancel out. If 6 is positive, then 6 minus 1 is 5, but if 6 is negative, then -6 minus 1 is -7. Hope this helps!

Let's say x + 6 = square root of 10. How would I do this if 10 isn't a square number?

This is a common scenario. Your results will have 2 terms. First, let's fix an error in what you've done so far. Quadratic equations generally have 2 solutions. You lost one of them. When you apply the square root to both sides of the equation, on the side with the 10, you need to ensure you have both the positive and negative root. x+6 = +/- sqrt(10) From here, you just need to subtract 6 from both sides of the equation. x = -6 +/- sqrt(10) Or, written individually, x = -6+sqrt(10) and x=-6-sqrt(10). Those are your solutions. Should you need to use them for graphing, you can do estimated values for the square roots, then subtract 6. Hope this helps.

how do you solve (x-7)^2-9=49? by extracting square root

Add 9 to both sides of the equation: `(x-7)^2=58` Take square root of both sides: `sqrt(x-7)^2 = +/- sqrt(58)` Simplify square roots: `x-7 = +/- sqrt(58)` Add 7 to both sides: `x = 7 +/- sqrt(58)` Hope this helps.

how to solve : -(-x+1)^2

Solving this is impossible without an equation. If they want you to simplify, remember PEMDAS. Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction. In this case, you can't really do anything in the Parenthesis, so you start with the exponent. First find what (-x+1) * (-x+1) is equal to. Then multiply everything by -1 to deal with the minus side at the beginning. If you are trying to solve the equation (or find the "0"s), set the equation equal to 0. From that point, you would treat it like anything else that looks like this. Multiply both sides by -1 to get: (-x+1)^2 = 0 From there, you should be able to use the review above to find your answer.

Do all quadratics always have two solutions?

No, not all quadratics have multiple solutions. In fact, some quadratic equations have no solutions. Here is how to tell how many solutions a quadratic equation has. Suppose we have a quadratic equation a*x^2+b*x+c=0. If b^2-4*a*c > 0, there are two solutions. If b^2-4*a*c = 0, there is one solution. If b^2-4*a*c < 0, there are no solutions.

can you use fancy quadratics skills for this

You can but it would take more time and be inefficient.

Main content

Algebra 1

Course: Algebra 1 > Unit 14

Lesson 3: Solving by taking the square root

Solving simple quadratics review

Q: can you use fancy quadratics skills for this

You can but it would take more time and be inefficient.

Google Classroom

Simple quadratic equations like x^2=4 can be solved by taking the square root. This article reviews several examples and gives you a chance to practice on your own.

In general, a quadratic equation can be written as:

a, x, squared, plus, b, x, plus, c, equals, 0

In this article, we review how to solve quadratics that are solvable by taking the square root—no fancy factoring or quadratic equations here; we'll get to that technique later.

Example 1

We're given 3, x, squared, minus, 7, equals, 5 and asked to solve for x.

We can show our work like this:

\begin{aligned} 3x^2-7&=5\\\\ 3x^2&=12\\\\ x^2&=4\\\\ \sqrt{x^2}&=\pm \sqrt{4}\\\\ x&=\pm 2 \end{aligned}

So our two solutions are:

x, equals, 2
x, equals, minus, 2

Notice the plus minus symbol we included when taking the square root of both sides. This symbol means "plus or minus," and it is important because it ensures we catch both solutions. Want a deeper explanation? Check out this video.

Let's check both solutions:

x, equals, 2	x, equals, minus, 2
$\begin{aligned}3x^2-7&=5\\\\3(2)^2-7&=5\\\\3\cdot4-7&=5\\\\12-7&=5\\\\5&=5\end{aligned}$	$\begin{aligned}3x^2-7&=5\\\\3(-2)^2-7&=5\\\\3\cdot4-7&=5\\\\12-7&=5\\\\5&=5\end{aligned}$

Yes! Both solutions check out.

Example 2

We're given left parenthesis, x, minus, 3, right parenthesis, squared, minus, 81, equals, 0 and asked to solve for x.

We can show our work like this:

\begin{aligned} (x - 3)^2 - 81 &= 0\\\\ (x - 3)^2 &= 81\\\\ \sqrt{(x - 3)^2} &= \pm \sqrt{81}\\\\ x - 3 &= \pm 9\\\\ x &= \pm 9+3 \end{aligned}

So our two solutions are:

x, equals, plus, 9, plus, 3, equals, start color #11accd, 12, end color #11accd
x, equals, minus, 9, plus, 3, equals, start color #11accd, minus, 6, end color #11accd

Let's check both solutions:

x, equals, start color #11accd, 12, end color #11accd	x, equals, start color #11accd, minus, 6, end color #11accd
$\begin{aligned}(x - 3)^2 - 81 &= 0\\\\(\blueD{12} - 3)^2 - 81 &= 0\\\\9^2 - 81 &= 0\\\\81 - 81 &= 0\\\\0 &= 0\end{aligned}$	$\begin{aligned}(x - 3)^2 - 81 &= 0\\\\(\blueD{-6} - 3)^2 - 81 &= 0\\\\(-9)^2 - 81 &= 0\\\\81 - 81 &= 0\\\\0 &= 0\end{aligned}$

Yep! Both check out.

Want to learn more about these types of problems? Check out this video.

Practice

Solve for x.

left parenthesis, x, plus, 1, right parenthesis, squared, minus, 36, equals, 0

(Choice A)
x, equals, minus, 5, comma, x, equals, 7
(Choice B)
x, equals, 5, comma, x, equals, 7
(Choice C)
x, equals, 5, comma, x, equals, minus, 7
(Choice D)
x, equals, minus, 5, comma, x, equals, minus, 7

Want more practice? Check out this exercise

Want to join the conversation?

Sort by:

Shiv
Posted 6 years ago. Direct link to Shiv's post “For the question, I got a...”
For the question, I got answer choice b?
Is that correct, because even though I got it correct, I feel like it is wrong. How can I check my answer? PLEASE HELP!
Button navigates to signup pageComment on Shiv's post “For the question, I got a...”
(13 votes)
Answer
- Stephen Earley
  Posted 3 years ago. Direct link to Stephen Earley's post “(x+1)^2 - 36 = (x+1)^2 =...”
  (x+1)^2 - 36
  
  = (x+1)^2 = 36 | *Add 36 to both sides to cancel out.
  
  = x+1 = +/-6 | *Take the plus-or-minus square root of both sides, since x could be positive or negative. 36 becomes plus-or-minus 6. If you would like a better understanding of this principle, watch this khan video. It explains it in detail starting at 1: 37.
  
  https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/v/simple-quadratic-equation
  
  x = either (6-1 = 5) or (-6-1 = -7) | *Subtract 1 from both sides to cancel out. If 6 is positive, then 6 minus 1 is 5, but if 6 is negative, then -6 minus 1 is -7.
  
  Hope this helps!
  Button navigates to signup page
  (8 votes)
xiao hu
Posted 4 months ago. Direct link to xiao hu's post “Let's say x + 6 = square ...”
Let's say x + 6 = square root of 10. How would I do this if 10 isn't a square number?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Kim Seidel
  Posted 4 months ago. Direct link to Kim Seidel's post “This is a common scenario...”
  This is a common scenario. Your results will have 2 terms.
  First, let's fix an error in what you've done so far. Quadratic equations generally have 2 solutions. You lost one of them.
  When you apply the square root to both sides of the equation, on the side with the 10, you need to ensure you have both the positive and negative root.
  x+6 = +/- sqrt(10)
  
  From here, you just need to subtract 6 from both sides of the equation.
  x = -6 +/- sqrt(10)
  
  Or, written individually, x = -6+sqrt(10) and x=-6-sqrt(10).
  Those are your solutions.
  
  Should you need to use them for graphing, you can do estimated values for the square roots, then subtract 6.
  
  Hope this helps.
  Button navigates to signup page
  (9 votes)
Lois
Posted 5 years ago. Direct link to Lois's post “how do you solve (x-7)^2-...”
how do you solve (x-7)^2-9=49?
by extracting square root
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “Add 9 to both sides of th...”
  Add 9 to both sides of the equation: (x-7)^2=58
  Take square root of both sides: sqrt(x-7)^2 = +/- sqrt(58)
  Simplify square roots: x-7 = +/- sqrt(58)
  Add 7 to both sides: x = 7 +/- sqrt(58)
  
  Hope this helps.
  Button navigates to signup page
  (8 votes)
bvargas-24
Posted 3 years ago. Direct link to bvargas-24's post “how can i get a better un...”
how can i get a better understanding
Button navigates to signup pageComment on bvargas-24's post “how can i get a better un...”
(3 votes)
Answer
csale
Posted 4 years ago. Direct link to csale's post “did I just accidentally d...”
did I just accidentally do the wrong course?
Button navigates to signup pageComment on csale's post “did I just accidentally d...”
(3 votes)
Answer
rathnamary.jacob
Posted 7 years ago. Direct link to rathnamary.jacob's post “how to solve : -(-x+1)^...”
how to solve : -(-x+1)^2
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- VincentTheFrugal
  Posted 7 years ago. Direct link to VincentTheFrugal's post “Solving this is impossibl...”
  Solving this is impossible without an equation. If they want you to simplify, remember PEMDAS. Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction.
  
  In this case, you can't really do anything in the Parenthesis, so you start with the exponent. First find what (-x+1) * (-x+1) is equal to. Then multiply everything by -1 to deal with the minus side at the beginning.
  
  If you are trying to solve the equation (or find the "0"s), set the equation equal to 0. From that point, you would treat it like anything else that looks like this. Multiply both sides by -1 to get:
  
  (-x+1)^2 = 0
  
  From there, you should be able to use the review above to find your answer.
  Button navigates to signup page
  (3 votes)
lschlottman
Posted 2 years ago. Direct link to lschlottman's post “How do I solve x^2-6x +8 ...”
How do I solve x^2-6x +8 = 0 by taking the square root? I know the solution is 2,4, but how do I use this method to solve?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- 👑💎 Professor Sykes 💎👑
  Posted 2 years ago. Direct link to 👑💎 Professor Sykes 💎👑's post “x^2-6x+8=0 As shown above...”
  x^2-6x+8=0
  As shown above you need to first simply the equation then put it in the quadratic form:
  x = -(-6)±√(-6)^2-4*8 / 2
  
  Then you square the -6 inside the parenthesis:
  x = -(-6)±√36-4*8 / 2
  
  Then multiply the -4 * 8:
  x = -(-6)±√36-32 / 2
  
  Subtract 36 and 32:
  x = -(-6)±√4 / 2
  
  Therefore take the square root of 4:
  x = -(-6)±2 / 2
  
  Opposite of -6 is 6:
  x = 6±2 / 2
  
  Then solve the equation for ± to be addition; 6+2:
  8/2
  
  x = 4
  
  Ok now solve equation when ± is subtraction; 6-2:
  x = 4/2
  
  x = 2
  
  solutions: 2 and 4 by using the quadratic formula.
  
  Hopes this helps you out.
  Comment on 👑💎 Professor Sykes 💎👑's post “x^2-6x+8=0 As shown above...”
  (1 vote)
Rebecca
Posted 4 years ago. Direct link to Rebecca's post “Do all quadratics always ...”
Do all quadratics always have two solutions?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- KLaudano
  Posted 4 years ago. Direct link to KLaudano's post “No, not all quadratics ha...”
  No, not all quadratics have multiple solutions. In fact, some quadratic equations have no solutions. Here is how to tell how many solutions a quadratic equation has.
  
  Suppose we have a quadratic equation a*x^2+b*x+c=0.
  
  If b^2-4*a*c > 0, there are two solutions.
  If b^2-4*a*c = 0, there is one solution.
  If b^2-4*a*c < 0, there are no solutions.
  Comment on KLaudano's post “No, not all quadratics ha...”
  (2 votes)
jlicina793
Posted 7 months ago. Direct link to jlicina793's post “All these problems on zer...”
All these problems on zero product are making me nauseous.
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
shuwenzhengnn
Posted 4 years ago. Direct link to shuwenzhengnn's post “can you use fancy quadrat...”
can you use fancy quadratics skills for this
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Saivishnu Tulugu
  Posted 4 years ago. Direct link to Saivishnu Tulugu's post “You can but it would take...”
  You can but it would take more time and be inefficient.
  Button navigates to signup page
  (3 votes)