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=−0.77 x equals negative 0.77 x=1.04 x equals 1.04 x=−1.85 x equals negative 1.85 x=1.15

Answer 1

To solve the quadratic equation \(4x^2 + 2x = 10\), we first rearrange it to standard form:

\[ 4x^2 + 2x - 10 = 0 \]

Next, we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 4\), \(b = 2\), and \(c = -10\).

Calculating the discriminant:

\[ b^2 - 4ac = 2^2 - 4 \cdot 4 \cdot (-10) = 4 + 160 = 164 \]

Now substituting into the quadratic formula:

\[ x = \frac{-2 \pm \sqrt{164}}{2 \cdot 4} \]

Calculating \(\sqrt{164}\):

\[ \sqrt{164} \approx 12.81 \]

Now substituting back into the formula:

\[ x = \frac{-2 \pm 12.81}{8} \]

Calculating the two potential solutions:

1. Using the plus sign:

\[ x = \frac{-2 + 12.81}{8} \approx \frac{10.81}{8} \approx 1.35 \]

2. Using the minus sign:

\[ x = \frac{-2 - 12.81}{8} \approx \frac{-14.81}{8} \approx -1.85 \]

Rounding to the nearest hundredth, we get:

• The solutions are approximately \(x \approx 1.35\) and \(x \approx -1.85\).

From the provided responses, \(x = -1.85\) matches one of the solutions.

Thus, the correct answer is:

x = −1.85