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

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Answer 1 · 2017-05-15T01:44:35

#x=-11# and #x=9#

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 #x#s:

#x=-11# and #x=9#