Question

Solve the equation by using the Quadratic Formula.

4⁢𝑥^2−6⁢𝑥=−2

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

First write in standard form: 4x^2 − 6x + 2 = 0.

Use the quadratic formula x = [−b ± sqrt(b^2 − 4ac)]/(2a) with a = 4, b = −6, c = 2:
x = [6 ± sqrt((-6)^2 − 4·4·2)]/(2·4)
= [6 ± sqrt(36 − 32)]/8
= [6 ± sqrt(4)]/8
= [6 ± 2]/8.

Thus x = (6−2)/8 = 4/8 = 1/2 or x = (6+2)/8 = 8/8 = 1.

Answer (least to greatest): 1/2, 1.