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.(1 point)
Responses
x=1.04
x equals 1.04
x=1.15
x equals 1.15
x=−1.85
x equals negative 1.85
x=−0.77
x equals negative 0.77
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To solve the quadratic equation 4x^2 + 2x = 10, we can rearrange it to the form ax^2 + bx + c = 0, where a = 4, b = 2, and c = -10. Then, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-2 ± √(2^2 - 4(4)(-10))) / (2(4))
= (-2 ± √(4 + 160)) / 8
= (-2 ± √164) / 8
Since we are given options rounded to the nearest hundredth, we can accurately evaluate this expression to:
x = (-2 ± 12.81) / 8
Simplifying further, we get:
x ≈ (-2 + 12.81) / 8 ≈ 10.81 / 8 ≈ 1.35
x ≈ (-2 - 12.81) / 8 ≈ -14.81 / 8 ≈ -1.85
Therefore, the solutions to the quadratic equation 4x^2 + 2x = 10 are approximately x = 1.35 and x = -1.85.
Out of the given options, the solution that matches is x = 1.15.