Question

Solve the equation by using the Quadratic Formula.

𝑥^2−𝑥−5=0

Simplify your solutions. If the solutions are real rational numbers, list from least to greatest separated by a comma. If the solutions are not real numbers, write your answer in the form a ± bi. If the solutions are irrational, write your answer in simplified radical form, using ± to express both solutions.

Answer 1

Use the quadratic formula x = [-b ± √(b^2 - 4ac)]/(2a) with a = 1, b = -1, c = -5:

x = [1 ± √(1 + 20)]/2 = [1 ± √21]/2.

So the solutions are (1 − √21)/2 and (1 + √21)/2 (or compactly (1 ± √21)/2).