Question

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

Answer 1

first expand the product.

(x+7)(x-9) = ?

Answer 2

x^2-9x+7x-63

Answer 3

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

Answer 4

Add 63 to both sides, and u then get?

Answer 5

-38

Answer 6

x\(^2\)-2x-63 = 25

x\(^2\)-2x-63\(\small\color{red}{+63}\)= 25\(\small\color{red}{+63}\)

Answer 7

like that, add 63 to both sides.
what do you get after doing this?

Answer 8

ooooooooooh i see.
x^2-2x= 88

Answer 9

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")

Answer 10

1?

Answer 11

that number that makes the left hand side a perfect square trinomial, this number, you should add to both sides of the equation.

Answer 12

yes, it is 1.

Answer 13

So, add 1 to both sides

Answer 14

x\(^2\)-2x\(\small\color{blue}{+1}\)= 88\(\small\color{blue}{+1}\)

Answer 15

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