Question

Use the completing the square method to find the roots of 4x2 + 28x = 32.

A) 8, 1

B) 8, -1

C) -8, 1

D) -8, -1

Answer 1

First ensure that the x^2 term has a coefficient of 1 by dividing every term by 4:
x^2 + 7x = 8
Then find the value of (b/2)^2 which is 12.25 or 49/4 (7/2)^2
Then add 49/4 to both sides:
x^2 + 7x + 49/4 = 81/4
Then factor the equation into:
(x + 7/2)^2 = 81/4
Apply the square root property:
+- (x + 7/2) = 9/2
Solve for x:
x - 7/2 = 9/2 for one root
x = 16/2
x + 7/2 = 9/2 for the other root
x = 2/2
So, roots are 8 and 1. Hope this helps!