Question

Which of the following is a solution to the quadratic equation 4x2+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=−1.85
x equals negative 1.85

x=1.04
x equals 1.04

x=1.15

Answer 1

To solve the quadratic equation \(4x^2 + 2x = 10\), we first rearrange it into 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 \(c = -10\).

Now we calculate the discriminant (\(b^2 - 4ac\)):

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

Now substitute the values into the quadratic formula:

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

Calculating \(\sqrt{164}\):

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

So we find:

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

Calculating the two possible values for \(x\):

1. \(x = \frac{-2 + 12.81}{8} = \frac{10.81}{8} \approx 1.35\)
2. \(x = \frac{-2 - 12.81}{8} = \frac{-14.81}{8} \approx -1.85\)

Thus, the approximate solutions to the equation rounded to the nearest hundredth are:

\[
x \approx 1.35 \quad \text{and} \quad x \approx -1.85
\]

From the given options, the solution \(x = -1.85\) is the correct one.