Question

Solve the equation by using the Quadratic Formula.

𝑥^2+8⁢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=8, c=5.

Discriminant = 8^2 − 4·1·5 = 64 − 20 = 44 = 4·11, so √44 = 2√11.

x = (-8 ± 2√11) / 2 = -4 ± √11.

Answers: x = -4 ± √11 (i.e. -4 − √11, -4 + √11).