The correct answer is: x = (-1 + √33) / 4
The quadratic equation can be solved using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 2, b = 1, and c = -4.
Substituting these values into the quadratic formula, we get:
x = (-1 ± √(1² - 4 * 2 * -4)) / 2 * 2
x = (-1 ± √33) / 4
Therefore, the solutions to the equation are:
x = (-1 + √33) / 4 or x = (-1 - √33) / 4
Checking the answers, we can see that both solutions satisfy the equation.
Therefore, the correct answer is:
x = (-1 + √33) / 4 or x = (-1 - √33) / 4