Solve the equation −7x2−10=−12x . Write your conjugate pair solution(s) as two values separated by a ± sign.(1 point) x=

To solve the equation \(-7x^2 - 10 = -12x\), we first rearrange the equation to standard quadratic form:

\[
-7x^2 + 12x - 10 = 0
\]

To make the calculations easier, we can multiply the entire equation by -1:

\[
7x^2 - 12x + 10 = 0
\]

Next, we will use the quadratic formula to find the solutions. The quadratic formula is:

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

In our equation, \(a = 7\), \(b = -12\), and \(c = 10\). We first calculate the discriminant \(b^2 - 4ac\):

\[
b^2 = (-12)^2 = 144
\]
\[
4ac = 4 \cdot 7 \cdot 10 = 280
\]
\[
b^2 - 4ac = 144 - 280 = -136
\]

Since the discriminant is negative, we will have complex conjugate solutions. Now let's calculate the solutions using the quadratic formula:

\[
x = \frac{-(-12) \pm \sqrt{-136}}{2 \cdot 7}
\]
\[
x = \frac{12 \pm \sqrt{-136}}{14}
\]

We can simplify \(\sqrt{-136}\) as follows:

\[
\sqrt{-136} = \sqrt{136} \cdot i = \sqrt{4 \cdot 34} \cdot i = 2\sqrt{34} \cdot i
\]

Substituting this back into the equation, we get:

\[
x = \frac{12 \pm 2\sqrt{34}i}{14}
\]
\[
x = \frac{12}{14} \pm \frac{2\sqrt{34}i}{14}
\]
\[
x = \frac{6}{7} \pm \frac{\sqrt{34}}{7}i
\]

Thus, the conjugate pair solutions are:

\[
x = \frac{6}{7} \pm \frac{\sqrt{34}}{7}i
\]

So the final answer is:

\[
x = \frac{6}{7} \pm \frac{\sqrt{34}}{7}i
\]