Final answer:
To solve the quadratic equation x² = 5x + 8, we can use the quadratic formula. The solutions for x are (5 + √57)/2 and (5 - √57)/2.
Step-by-step explanation:
To solve the quadratic equation x² = 5x + 8, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b²-4ac))/(2a)
In this case, a = 1, b = -5, and c = -8. Plugging these values into the formula, we get:
x = (-(-5) ± √((-5)²-4(1)(-8)))/(2(1))
Simplifying further:
x = (5 ± √(25+32))/2
x = (5 ± √57)/2
Therefore, the solutions for x are:
x = (5 + √57)/2
x = (5 - √57)/2