Answer:
x = sqrt(17)/8 - 1/8 or x = -1/8 - sqrt(17)/8
Step-by-step explanation using the quadratic formula:
Solve for x over the real numbers:
4 x^2 + x - 1 = 0
Divide both sides by 4:
x^2 + x/4 - 1/4 = 0
Add 1/4 to both sides:
x^2 + x/4 = 1/4
Add 1/64 to both sides:
x^2 + x/4 + 1/64 = 17/64
Write the left hand side as a square:
(x + 1/8)^2 = 17/64
Take the square root of both sides:
x + 1/8 = sqrt(17)/8 or x + 1/8 = -sqrt(17)/8
Subtract 1/8 from both sides:
x = sqrt(17)/8 - 1/8 or x + 1/8 = -sqrt(17)/8
Subtract 1/8 from both sides:
Answer: x = sqrt(17)/8 - 1/8 or x = -1/8 - sqrt(17)/8
