Answer:
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In the equation 2x^2 + 2x - 1 = 0, we have:
a = 2
b = 2
c = -1
Substituting these values into the formula, we get:
x = (-2 ± sqrt(2^2 - 4(2)(-1))) / (2)(2)
Simplifying this expression, we get:
x = (-2 ± sqrt(4 + 8)) / 4
x = (-2 ± sqrt(12)) / 4
x = (-2 ± 2sqrt(3)) / 4
x = (-1 ± sqrt(3)) / 2
Therefore, the solutions to the equation 2x^2 + 2x - 1 = 0 are:
x = (-1 + sqrt(3)) / 2
x = (-1 - sqrt(3)) / 2