How do you solve using completing the square method #x^2 - 3x = 18#?

1 Answer
Apr 6, 2016

Answer:

#x= -3 #
#x= 6#

Explanation:

Note: The goal of completing the square is to create a perfect trinomial in the form of

#(a^2 +2ab+b^2) = (a+b)^2# # " " " or#
#(a^2 -2ab+b^2) = (a-b)^2#

Given:

#x^2 - 3x = 18#

Step 1: The leading coefficient is 1, we can proceed to the next step of completing the square

Step 2: The third term is , #[(1/2)(-3)]^2 = 9/4#

#x^2 - 3x + [(1/2)(-3)]^2 = 18 + [(1/2)(-3)]^2#

#x^2 - 3x +color(red)(9/4) = 18 + color(red)(9/4)#

Step 3: Rewrite as a perfect trinomial on the left and simplify the right side of the equation

#x^2 -3x +(3/2)^2 = 18/1 + 9/4 #

#(x-3/2)^2= 72/4 +9/4#

#(x-3/2)^2 = 81/4 #

Step 4: Solve the equation by taking the square root of both side
remember #sqrt(x^2) = +-x#

#sqrt((x-3/2)^2) = sqrt(81/4)#

#x-3/2 = +-9/2 #

Step 5: Then solve for #x#

#x = -9/2 + 3/2# # " " or " # #x= 9/2 +3/2#

So # " " x= -6/2 = -3#

or # " " x= 12/2 = 6#