Question

Which of the following is the solution to the quadratic equation 4x squared + 2x = 10 ascended to solution has been rounded to the nearest hundredth if applicable
X = -0.77 x = 1.15 X = 1.04 X = -1.85

Answer 1

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

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

Next, we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this equation, \( a = 4 \), \( b = 2 \), and \( c = -10 \). Now, we can substitute these values into the formula:

1. Calculate the discriminant (\( b^2 - 4ac \)):
\[
b^2 = 2^2 = 4
\]
\[
4ac = 4 \cdot 4 \cdot (-10) = -160
\]
\[
b^2 - 4ac = 4 - (-160) = 4 + 160 = 164
\]

2. Now, calculate the square root of the discriminant:
\[
\sqrt{164} \approx 12.81
\]

3. Substitute back into the quadratic formula:
\[
x = \frac{-2 \pm 12.81}{2 \cdot 4}
\]
\[
x = \frac{-2 \pm 12.81}{8}
\]

Now we can calculate the two possible solutions:

1. For \( x = \frac{-2 + 12.81}{8} \):
\[
x = \frac{10.81}{8} \approx 1.35
\]

2. For \( x = \frac{-2 - 12.81}{8} \):
\[
x = \frac{-14.81}{8} \approx -1.85
\]

Thus, rounding to the nearest hundredth, the solutions are approximately \( x \approx 1.35 \) and \( x \approx -1.85 \).

Among the choices you provided:
- \( x = -0.77 \)
- \( x = 1.15 \)
- \( x = 1.04 \)
- **\( x = -1.85 \)**

The correct solution to the quadratic equation rounded to the nearest hundredth is \( x = -1.85 \).