Question

b. $7x^2 - 5x + 7 = -2$

Explanation:

Step1: Rearrange to standard quadratic form

Add 2 to both sides to set equation to 0.
$7x^2 - 5x + 7 + 2 = 0$
$7x^2 - 5x + 9 = 0$

Step2: Identify quadratic coefficients

For $ax^2+bx+c=0$, define $a=7$, $b=-5$, $c=9$.

Step3: Use quadratic formula

Apply $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.
$x=\frac{-(-5)\pm\sqrt{(-5)^2-4(7)(9)}}{2(7)}$

Step4: Compute discriminant and simplify

Calculate discriminant and final terms.
$\sqrt{25 - 252}=\sqrt{-227}=i\sqrt{227}$
$x=\frac{5\pm i\sqrt{227}}{14}$

Answer:

$x=\frac{5 + i\sqrt{227}}{14}$ and $x=\frac{5 - i\sqrt{227}}{14}$