If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Get ready for Algebra 2>Unit 2

Lesson 7: Solving quadratic equations by taking the square root

# Solving quadratics by taking square roots examples

Sal solves the equation (x+3)²-4=0 and finds the x-intercepts of f(x)=(x-2)²-9.

## Want to join the conversation?

• kindly help i this confusion
(x+7)^2-49=0
(x+7)=+/-7
x=0 or -14
BUT COULDN'T I DO THE FOLLOWING
(x+7)^2-49=0
x^2+14x+49-49=0
x^2+14x=0, then x^2=-14x , divide both sides by x
x=-14
in this i cant discover x=0, how this could happen?! how to follow valid steps and miss one of the solutions ?
• Never divide by the variable. You destroy / lose solutions to the equation.
Instead, use factoring: x^2+14x=0 becomes x(x+14)=0
Use zero product rule: x=0 and x+14=0
Solutions become: x=0 and x=-14

Hope this helps.
• it a parabola is open upwards what does it repersent? (in terms of a throwing arc)
• I just realized that it could represent a ball being thrown into water because it could come back up.
• How are you supposed to solve equations that have square rooted prime numbers?

[Example: x + 8 = ^2]
• You cannot combine numbers and roots, so by subtracting 8, the answer would be x = - 8 + √2. You can get an approximation if you need to, but the exact answer is as above.
• So, would there be an actual way to figure out only one answer.
• you can not figure out only one answer because it has 2 answers.
(1 vote)
• how f(x)=(x-2)^2-9 is a function ?
as sal said that functions can only have one output then how can a parabola be a function...?
• A function generates only one output (y-value) for each input value (x-value).
The equation f(x)=(x-2)^2-9 satisfies that requirement. Each time you input a value for "x", you only get one value for "y".

I think you may be confusing "x" and "y". Parabolas will have the same "y" value for 2 different "x" values. That's ok. "y" is not the input.
• Do you think he started the video a little too late? He doesn't give his usual intro in this video.
• how do i add a square root symbol
• On KhanAcademy, if your answer needs to include a square root, then a menu of special symbols is provided when your cursor is in the answer box. If no option is provided, then likely you haven't simplified your answer. For example: sqrt(49) would not be an appropriate answer because it simplifies to 7.

Hope this helps.
• Wouldn't it be 'and'? x=-1 and x=-5. My reasoning: It is a parabola and there are two x intercepts.
• I'm not sure what your reasoning mean, since if its an actual reasoning, it will also apply to using 'or'.

x = -1 or x = -5 means the x-value when f(x) = 0. You can't have a point with 2 x-values.
You use x = -1 and x = -5 when you are describing the parabola, so you say
f(x) has 2 x-intercepts, x = -1 and x = -5.
• what if it can't be square rooted? like ((x−6)^2)−5=0
5 can't be square rooted.
(1 vote)
• The 5 can be square rooted. It is just an irrational number which we leave as sqrt(5) unless we need an estimated value. Then we would use a calculator to get the estimate.
You equation has solutions of: x = 6 +/- sqrt(5)

Hope this helps.
• SO, since u got (x+3)^2=4. IS there's another way to do this ? I tried multiply ways

-U would go head and solve x+3^2 which could be 3x^2 or 9x=4 so that wont work
Also u can distributed x+3^2 to be 2x+9=4
-subtract by 9 which would be 2x=-5 that wont work either
(1 vote)
• 1) You can solve using square root method, as shown in the video.
2) You can simplify the equation and then factor. This is what you were trying to do, But, you are confusing what (x+3)^2 means. Here are the steps:
-- (x+3)^2 means (x+3)(x+3. Use FOIL, or distributive property to multiply it out.
`(x+3)(x+3)=4`
`x^2 + 3x + 3x + 9 = 4`
`x^2 + 6x + 9 = 4`
-- Subtract 4 from both sides:
`x^2 + 6x + 9 -4 = 4 - 4`
`x^2 + 6x + 5 = 0`
-- Factor the trinomial: find factors of 4 that also add to 6. Use 5 and 1
`(x+5)(x+1) = 0`
-- Use the zero product rule. Split the factors and set each individually = 0 and solve
`x + 5 = 0` creates `x = -5`
`x + 1 = 0` creates `x = -1`

You will later learn that you can also solve the equation by completing the square and by the quadratic formula.
Hope this helps.