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

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

Explanation:

Answer 2

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 squares4*(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