Question

1. $x^{2}=8x+14$

Explanation:

Step1: Rearrange to standard quadratic form

$x^2 - 8x - 14 = 0$

Step2: Identify coefficients for quadratic formula

For $ax^2+bx+c=0$, $a=1$, $b=-8$, $c=-14$

Step3: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(-14)}}{2(1)}$

Step4: Calculate discriminant and simplify

$\sqrt{64 + 56}=\sqrt{120}=2\sqrt{30}$
$x=\frac{8\pm2\sqrt{30}}{2}$

Step5: Simplify the fraction

$x=4\pm\sqrt{30}$

Answer:

$x=4+\sqrt{30}$ or $x=4-\sqrt{30}$