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.
A. x = -1.85
B. x = 1.15
C. x = 1.04
D. x = -0.77
To find the solutions to the quadratic equation 4x^2 + 2x = 10, we first need to rearrange the equation to the standard form of a quadratic equation: 4x^2 + 2x - 10 = 0.
Next, we can solve the quadratic equation either by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
Given a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants with a ≠ 0, the solutions to the quadratic equation are given by the formula: x = (-b ± √(b^2 - 4ac)) / (2a).
For our equation 4x^2 + 2x - 10 = 0, we can identify that a = 4, b = 2, and c = -10.
Using the quadratic formula, we can calculate the solutions:
x = (-2 ± √(2^2 - 4 * 4 * -10)) / (2 * 4)
= (-2 ± √(4 + 160)) / 8
= (-2 ± √164) / 8
≈ (-2 ± 12.81) / 8
Now, let's round the solutions to the nearest hundredth:
x ≈ (-2 + 12.81) / 8 ≈ 10.81 / 8 ≈ 1.35
x ≈ (-2 - 12.81) / 8 ≈ -14.81 / 8 ≈ -1.85
The approximate solutions to the quadratic equation 4x^2 + 2x = 10 are x ≈ 1.35 and x ≈ -1.85.
Comparing these solutions to the given options, we can see that the correct solution is A. x = -1.85.