Question

Solve the equation by using the Quadratic Formula.

16⁢𝑥^2−24⁢𝑥−25=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=16, b=−24, c=−25.

Discriminant: b^2 − 4ac = (−24)^2 − 4(16)(−25) = 576 + 1600 = 2176 = 64·34, so √2176 = 8√34.

x = [24 ± 8√34]/32 = [3 ± √34]/4.

Hence the solutions are (3 − √34)/4, (3 + √34)/4 (or compactly (3 ± √34)/4).