Question

Solve the quadratic equation by completing the square. What are the missing pieces to the steps? –27 = 4x2 – 24x –27 = 4(x2 – 6x) –27 + = 4(x2 – 6x + 9) 9 = 4(x – 3)2 = (x – 3)2 ± = x – 3 = x

Answer 1

We have that
4x² – 24x+27=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(4x² – 24x)=-27

Factor the leading coefficient 

4*(x² – 6x)=-27

Complete the square. Remember to balance the equation by adding the same constants to each side

4*(x² – 6x+9)=-27+36--------> missing pieces

Rewrite as perfect squares

4*(x-3)²=9

(x-3)²=9/4----> square root both sides----> (+/-)(x-3)=3/2----> missing pieces

+(x-3)=3/2------> x=(3/2)+3-----> x=9/2

-(x-3)=3/2-----> x=3-(3/2)-----> x=3/2

Answer 2

Answer:

36, 3/2, 3/2 and 9/2

Step-by-step explanation: