solve for x in the equation $x^{2}-14x + 31=63$.\n$x=-16$ or $x = 2$\n$x=-7pm3sqrt{7}$\n$x=-2$ or $x =…

Explanation:

Step1: Rearrange the equation

First, rewrite the given equation $x^{2}-14x + 31=63$ in standard quadratic - form $ax^{2}+bx + c = 0$. Subtract 63 from both sides: $x^{2}-14x+31 - 63=0$ $x^{2}-14x - 32 = 0$

Step2: Factor the quadratic equation

For a quadratic equation $x^{2}+bx + c=0$, we need to find two numbers that multiply to $c$ and add up to $b$. For $x^{2}-14x - 32 = 0$, we need two numbers that multiply to - 32 and add up to - 14. The numbers are - 16 and 2. So, $x^{2}-14x - 32=(x - 16)(x + 2)=0$

Step3: Solve for x

Set each factor equal to zero: If $x - 16=0$, then $x = 16$; if $x+2 = 0$, then $x=-2$

Answer:

$x=-2$ or $x = 16$