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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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  • aqualine ultimate style avatar for user mimicuabome
    Could you do the distributive property for this?
    (8 votes)
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    • female robot grace style avatar for user 17leed
      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
      (6 votes)
  • leaf green style avatar for user Nancy Nahra
    I saw the answer, but I couldn't tell how to indicate my answer for the correct sequence.
    (5 votes)
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    • spunky sam red style avatar for user MYSTO(AKA Ni-trip)
      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
      (3 votes)
  • aqualine sapling style avatar for user Jania
    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?
    (3 votes)
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  • male robot hal style avatar for user Sun
    At , what does Sal mean when Sal said "hold the equality?"
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      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.
      (3 votes)
  • male robot hal style avatar for user Sun
    I notice that when we are solving equations like that, it looks like Sal did a reversed PEMDAS rule (or SADMEP)! Is this true?
    (2 votes)
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    • mr pink green style avatar for user David Severin
      Not quite, he divided first, then he did the exponent then finally subtraction, so it was not quite reversed. He isolated the variable rather than reverse PEMDAS. So if you think about it, he reverses closest to x to farthest away. So add 4, square, and multiply by 2, so reverse opposites would be to divide by 2, take square root including ±, then subtract 4.
      (3 votes)
  • blobby green style avatar for user irisgomez789
    I need help 9(9-9x^2)= 9 I don't know how to solve this
    (2 votes)
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    • mr pink green style avatar for user David Severin
      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)
  • duskpin ultimate style avatar for user tobtobthebobe
    At in the lower left corner, what does "Sal said "square root of 11" but meant "11" " mean?
    (2 votes)
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  • blobby green style avatar for user Ife
    how do i solve x^2+8x=64=12
    (2 votes)
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  • blobby green style avatar for user m1538
    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)
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    • stelly blue style avatar for user Kim Seidel
      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)
  • male robot hal style avatar for user Sun
    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)
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    • stelly blue style avatar for user Kim Seidel
      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)

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.