Solve by completing the square,
8x^2+4x-4=0
divide by 8 and re-arrange
x^2 + (1/2)x = 1/2
x^2 + (1/2)x + 1/16 = 1/2 + 1/16
(x + 1/4)^2 = 9/16
x + 1/4 = ± 3/4
x = -1/4 ± 3/4
= 1/2 or -1
Reiny,
Im sorry but where is the 1/16 coming from?
take half of the middle coefficient , the square it
1/2 of 1/2 is 1/4
1/4 squared is 1/16
I added that to both sides, thus not changing the value of my equation.
To solve the quadratic equation 8x^2 + 4x - 4 = 0 by completing the square, follow these steps:
1. Move the constant term (the term without x) to the other side of the equation:
8x^2 + 4x = 4
2. Divide the entire equation by the coefficient of x^2 to make the leading coefficient 1:
x^2 + (4/8)x = 4/8
Simplify the equation:
x^2 + (1/2)x = 1/2
3. To complete the square, take half of the coefficient of x and square it, then add it to both sides of the equation.
Half of (1/2) is (1/4), and squaring it gives (1/4)^2 = 1/16.
Add 1/16 to both sides of the equation:
x^2 + (1/2)x + 1/16 = 1/2 + 1/16
Simplify:
x^2 + (1/2)x + 1/16 = 8/16 + 1/16
x^2 + (1/2)x + 1/16 = 9/16
4. Factor the left side of the equation as a perfect square:
The left side is (x + 1/4)^2.
(x + 1/4)^2 = 9/16
5. Take the square root of both sides of the equation, remembering to consider both the positive and negative square root:
x + 1/4 = ±√(9/16)
x + 1/4 = ±3/4
6. Solve for x:
Set x + 1/4 = 3/4 and solve:
x + 1/4 = 3/4
x = 3/4 - 1/4
x = 2/4
x = 1/2
Set x + 1/4 = -3/4 and solve:
x + 1/4 = -3/4
x = -3/4 - 1/4
x = -4/4
x = -1
The solutions to the equation 8x^2 + 4x - 4 = 0 are x = 1/2 and x = -1.