Question

solve the equation - 7x^2 - 10=-12x. express your solution(s) as a conjugate pair using ±

Explanation:

Step1: Rearrange the equation

First, rewrite the equation $-7x^{2}-10=-12x$ in standard quadratic - form $ax^{2}+bx + c = 0$. So, we get $7x^{2}-12x + 10 = 0$.

Step2: Identify coefficients

For the quadratic equation $7x^{2}-12x + 10 = 0$, we have $a = 7$, $b=-12$, and $c = 10$.

Step3: Use the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values of $a$, $b$, and $c$ into the formula:
\[

$$\begin{align*} x&=\frac{-(-12)\pm\sqrt{(-12)^{2}-4\times7\times10}}{2\times7}\\ &=\frac{12\pm\sqrt{144 - 280}}{14}\\ &=\frac{12\pm\sqrt{- 136}}{14}\\ &=\frac{12\pm2\sqrt{34}i}{14}\\ &=\frac{6\pm\sqrt{34}i}{7} \end{align*}$$

\]

Answer:

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