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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.

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• I saw the answer, but I couldn't tell how to indicate my answer for the correct sequence.
• 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
(1 vote)
• At in the lower left corner, what does "Sal said "square root of 11" but meant "11" " mean?
• 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.
• At you 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?
• 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.
• 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?
• 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.
• 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"?
• 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.
• Could you do the distributive property for this?
• 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
• In the Integrated Math 2 course, unit 3, lesson 3, the "Quadractics by taking square roots: strategy" exercise is after the video for "Solving quadratics by taking square roots: with steps." The "Quadratics by taking square roots: with steps" exercise is after the video for "Quadractics by taking square roots: strategy." This seems mixed up to me. Was this format made on purpose?
• it seems that the exercise order in the Integrated Math 2 course, unit 3, lesson 3, may be mixed up. The "Quadratics by taking square roots: strategy" exercise is listed after the video for "Solving quadratics by taking square roots: with steps," and the "Quadratics by taking square roots: with steps" exercise is listed after the video for "Quadratics by taking square roots: strategy." This may be an error in the course design, and it may be worth bringing it to the attention of the support team.
• 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.