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=1.15 x equals 1.15 x=1.04 x equals 1.04 x=−1.85 x equals negative 1.85 x=−0.77
To find the solutions to the quadratic equation 4x^2+2x=10, we first need to rearrange the equation to the form 4x^2+2x-10=0.
Then, we can use the quadratic formula to find the solutions, which is given by x = (-b ± √(b^2-4ac))/(2a).
For this equation, the values of a, b, and c are as follows:
a = 4
b = 2
c = -10
Substituting these values into the quadratic formula, we get:
x = (-2 ± √(2^2-4*4*(-10)))/(2*4)
x = (-2 ± √(4+160))/8
x = (-2 ± √164)/8
x = (-2 ± 12.81)/8
Rounding to the nearest hundredth, we get two possible solutions:
x ≈ (-2 + 12.81)/8 ≈ 1.04
x ≈ (-2 - 12.81)/8 ≈ -1.85
Therefore, the solutions to the quadratic equation 4x^2+2x=10 are x = 1.04 and x = -1.85.