Question

1. $x^{2}-10x + 36 = 2$

$x^{2}=-10x + 36 - 2=0$
$x^{2}=-10x + 38 = 0$
$x=-10x+25 + 38 - 25 = 0$
$\frac{10}{2}=5$ $(5)^{2}=25$
$(x + 5)(x + 9)=25$
$(x + 5)^{2}=sqrt{63}$
$5m^{2}-140 = 3m$

Explanation:

Step1: Rewrite the equation in standard form

Given $x^{2}-10x + 36=2$, we rewrite it as $x^{2}-10x+34 = 0$.

Step2: Use the quadratic formula

The quadratic formula for a quadratic equation $ax^{2}+bx + c=0$ is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a = 1$, $b=-10$, and $c = 34$.
First, calculate the discriminant $\Delta=b^{2}-4ac=(-10)^{2}-4\times1\times34=100 - 136=-36$.
Then, $x=\frac{10\pm\sqrt{-36}}{2}=\frac{10\pm6i}{2}=5\pm3i$.

Answer:

$x = 5\pm3i$