Solve the quadratic equation by completing the square.

4x2 + 2x - 7 = 0

A) x = 1 ± square root of 29/4
B) x = −1 ± square root of 29/4
C) x = −1 ± square root of 29/8
D) x = −1 ± square root of 29/16

Please help me!

1 answer

4x2 + 2x - 7 = 0
4 x^2 + 2 x = 7
x^2 + (1/2)x = 7/4
x^2 + (1/2) x +(1/4)^2 = 7/4 + 1/16 = (28+1)/16
(x+1/4)^2 = 29/16
x+1/4 = +/- sqrt(29/16) = +/- (1/4)sqrt(29)
x = [ -1 +/- sqrt(29) ] / 4

be more careful with parentheses