Question

Which of the following is a solution to the quadratic equation 4x^2 + 2x = 10? Assume that the solution has been rounded to the nearest hundredth, if applicable.
x = -1.85
x = -0.77
x = 1.04
x = 1.15

Answer 1

Solve 4x^2 + 2x − 10 = 0 → divide by 2: 2x^2 + x − 5 = 0.

x = [−1 ± sqrt(1 + 40)]/4 = (−1 ± sqrt 41)/4.
sqrt 41 ≈ 6.4031, so x ≈ (−1 ± 6.4031)/4 giving x ≈ 1.35078 and x ≈ −1.85078.

Rounded to the nearest hundredth: x ≈ 1.35 and x ≈ −1.85. From the choices, x = −1.85.