Question

Solve the equation by using the Quadratic Formula.

𝑥^2−14⁢𝑥+53=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 = [14 ± sqrt(14^2 − 4·1·53)]/2.

Compute the discriminant: 14^2 − 4·53 = 196 − 212 = −16, so
x = [14 ± sqrt(−16)]/2 = [14 ± 4i]/2 = 7 ± 2i.

Answer: 7 ± 2i.