anonymous
  • anonymous
Use completing the square to solve (x + 7)(x – 9) = 25 for x.
Mathematics
katieb
  • katieb
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SolomonZelman
  • SolomonZelman
first expand the product. (x+7)(x-9) = ?
anonymous
  • anonymous
x^2-9x+7x-63
SolomonZelman
  • SolomonZelman
yes, (x + 7)(x – 9) = 25 x\(^2\)-9x+7x-63 = 25 add the x's on the left side, x\(^2\)-2x-63 = 25

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SolomonZelman
  • SolomonZelman
Add 63 to both sides, and u then get?
anonymous
  • anonymous
-38
SolomonZelman
  • SolomonZelman
x\(^2\)-2x-63 = 25 x\(^2\)-2x-63\(\small\color{red}{+63}\)= 25\(\small\color{red}{+63}\)
SolomonZelman
  • SolomonZelman
like that, add 63 to both sides. what do you get after doing this?
anonymous
  • anonymous
ooooooooooh i see. x^2-2x= 88
SolomonZelman
  • SolomonZelman
yes, and then tell me what number would make the x²-2x +what a perfect square trinomial? (remember the rule DanJS posted: "half of the coefficient on x, then squared")
anonymous
  • anonymous
1?
SolomonZelman
  • SolomonZelman
that number that makes the left hand side a perfect square trinomial, this number, you should add to both sides of the equation.
SolomonZelman
  • SolomonZelman
yes, it is 1.
SolomonZelman
  • SolomonZelman
So, add 1 to both sides
SolomonZelman
  • SolomonZelman
x\(^2\)-2x\(\small\color{blue}{+1}\)= 88\(\small\color{blue}{+1}\)
SolomonZelman
  • SolomonZelman
can you go on from here? steps just in case: \(1.\) simplify the right side \(2.\) factor the left side (it should look like " (x-number)² ") \(3.\) take the square root of both sides (and don't forget the \(\pm\)) \(4.\) add 1 to both sides of the equation

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