Factor and find what x=

Divide both sides by 4 to get

4x^2 +4x -1 = 0

 

Quadratic Formula:      (-4 +- sqrt( 16+16) )/ 8 = -1/2 +-( sqrt32) /8

-1/2 +- (4 sqrt2)/8   =    -1/2 +- 1/2 sqrt2

Solve for x:
16 x^2+16 x-4 = 0

Divide both sides by 16:
x^2+x-1/4 = 0

Add 1/4 to both sides:
x^2+x = 1/4

Add 1/4 to both sides:
x^2+x+1/4 = 1/2

Write the left hand side as a square:
(x+1/2)^2 = 1/2

Take the square root of both sides:
x+1/2 = 1/sqrt(2) or x+1/2 = -1/sqrt(2)

Subtract 1/2 from both sides:
x = 1/sqrt(2)-1/2 or x+1/2 = -1/sqrt(2)

Subtract 1/2 from both sides:
Answer: |  x = 1/sqrt(2)-1/2        or           x = -1/2-1/sqrt(2)