How do you solve \frac { ( x + 9) ( x - 7) } { 2} = 18?

1 Answer
May 15, 2017

x=-11 and x=9

Explanation:

Multiply both sides by 2:

(x+9)(x-7)=36

Now expand the left side:

x^2+2x-63=36

Add 63 on both sides:

x^2+2x=99

Complete the square by adding (2/(1(2)))^2 on both sides. That evaluates to 1:

x^2+2x+1=100

Factor the left side:

(x+1)^2=100

Square root both sides. Remember that you will have a positive and negative solution:

x+1=+-sqrt(100)

Solve for x:

x=-1+-sqrt(100)

Evaluate sqrt(100):

x=-1+-10

Solve for the two xs:

x=-11 and x=9