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## Algebra 1

### Course: Algebra 1 > Unit 14

Lesson 3: Solving by taking the square root- Solving quadratics by taking square roots
- Solving quadratics by taking square roots
- Quadratics by taking square roots (intro)
- Solving quadratics by taking square roots examples
- Quadratics by taking square roots
- Quadratics by taking square roots: strategy
- Quadratics by taking square roots: strategy
- Solving quadratics by taking square roots: with steps
- Quadratics by taking square roots: with steps
- Solving simple quadratics review

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# Quadratics by taking square roots: strategy

Sal analyzes a given solution of a quadratic equation, and finds where and what was the error in that process. Created by Sal Khan.

## Want to join the conversation?

- I saw the answer, but I couldn't tell how to indicate my answer for the correct sequence.(4 votes)
- it may look comfusing at first, but it's all about looking at the question carefully! for example, the question that Sal was doing: it's obvious that the first line on the top won't be wrong, cause that IS the starting question! so the 1st step is obviously the 2nd line from the top, and 2nd step is the 3rd line from the top and so on. in short, whatever line it is in that kind of form, go down one line more to find the answer. Hope I am not confusing :P(2 votes)

- At1:33in the lower left corner, what does "Sal said "square root of 11" but meant "11" " mean?(2 votes)
- It is letting you know that when he said "square root of 11" it was a mistake and what he really meant is "11". Hope this helps.(2 votes)

- At0:27you said to try it out on your own, and I did........ The answer that I got was she did not do the negative and minus sign. Is that correct?(2 votes)
- Yes. She didn't put those in, and therefore only got one answer. To get the correct answer, the plus/minus sign must be there.(2 votes)

- The question is find all the roots. But i do not understand what that means exactly. One of the the questions is x^4 + x^2 - 90. The only thing that i could think of was x^6 - 90 but not any further than that. Is there a certain formula for this or am I correct?(2 votes)
- First, you can't add unlike terms: x^4 + x^2 does not = x^6

Next, I assume you have an equation of`y = x^4 + x^2 - 90`

or`f(x) = x^4 + x^2 - 90`

To find the roots, set y = 0 and solve for "x":`0 = x^4 + x^2 - 90`

Start by factoring. Your polynomial is factorable into`0 = (x^2 + 10)(x^2 - 9)`

You now have 2 quadratic factors. You can split these into individual equations to solve:`0 = x^2 + 10`

and`0 = x^2 - 9`

Both of these are solvable using the square root method shown in this video.

See if you can finish solving them. Note: One creates complex roots.

If you get stuck, comment back.(2 votes)

- Meredith actually solved the equation correctly on all of these steps, so I thought Meredith didn't make any mistakes! Did Meredith make a mistake in any of these steps? If yes, which step did Meredith made a mistake in? If not, then what happen to the choice "Meredith did not make a mistake"?(2 votes)
- This is an older version of KA's site. Many exercises like this now do include an option for no mistakes. Note: If that option isn't one of the possible answers, then you know that Meredith
**did**make a mistake. You just have to figure out where it is.(2 votes)

- Could you do the distributive property for this?(0 votes)
- You can't use distributive property for binomials like (x-2)^2 and then making it into x^2 - 2^2. There is a plus or minus within the brackets so apparently it is not possible. The next exercise will tell you so.

But if you have something like (x*2)^2 where you're multiplying terms, then you could distribute: x^2 * 2^2(5 votes)

- I need help 9(9-9x^2)= 9 I don't know how to solve this(1 vote)
- Distribute first 9*9 - 9*9x^2 = 9, 81 - 81x^2 = 9; add 81x^2 to both sides and subtract 9, you end up with 72 = 81x^2, divide by 81 to get x^2 = 72/81, square root of both sides, you get x = ± √(72/81) which reduces to x = ± √(8/9) = ± 2√2 / 3.(3 votes)

- how do i solve x^2+8x=64=12(1 vote)
- You need to clarify your equation. It has two "=" symbols. Is one suppose to be a minus?(2 votes)

- At0:37, what does Sal mean when Sal said "hold the equality?"(1 vote)
- Read the transcript as a whole sentence, not just the fragment. He is basically saying that the both sides were correctly divided by 2. This is required to maintain the equality of the equation (keep the 2 sides in balance / equal to each other).

Hope this helps.(2 votes)

- I remember learning about the zero product quality before, and I know that the problems weren't as easy. Like you were just given a quadratic equation in standard form and you had to turn it into a problem you can use the square root strategy on. Can anyone remind me how you'd do it in a scenario like that?(1 vote)
- The zero product rule is used when a quadratic is factored such as (x-7)(x+15)=0. In order for quantites to equal zero, one or more of them must be zero, so x-7=0 or x+15=0. The zero product rule does not apply on completing the square, the thing to use here is when you take square root of the constant, you have to include the ± sign.(1 vote)

## Video transcript

Meredith is solving the
following problem for homework, 2 times the quantity x plus
4 squared is equal to 242. She completes the problem
as seen in the steps below, and they give us the
steps right over here. When she gets to
school the next day, her teacher tells her that
the answer's x equals 7 and x equals negative 15. She only got x equals 7 here. In what step did
she make an error? So this first step
right here-- and I encourage you to
pause this video and try to figure
this out on your own before I work through it. So this first step, let's see. She got rid of this 2 by
dividing the left-hand side by 2, and she
appropriately divided. Well, you can't just
do that to one side. You have to do
that to both sides in order to hold this equality. So she divided 242 by 2 as
well, so that is correct. Step one makes sense. And then she just
wanted-- instead of this being an
x plus 4 squared, she wanted it to be an x plus 4. So she attempted to take the
square root of both sides. She said hey, look. The square root of x plus
4 squared is x plus 4, and the square
root of 121 is 11. And this is where she made
a small but very, very, very, very important mistake. Because if something
squared is equal to 121, that means that
something could be the positive or negative
square root of 121. This thing that we're
squaring could be positive 11, because positive
11 squared is 121, or x plus 4 right over
here could be negative 11, because negative 11
squared is also 121. So this right over here,
this should say x plus 4 is equal to the positive or
negative square root of 11, and so that's why she missed out
on one of the solutions right over here. So she messed up in step two. She should have taken
the positive and negative square root. So, we got that right.