what is $x^{2}-6 = 16x + 30$ rewritten in standard form, then factored? what value(s) of $x$ make the…

Answer:

1. Standard - form and factored form:
   • Standard form: $x^{2}-16x - 36=0$
   • Factored form: $(x - 18)(x+2)=0$
2. Values of $x$: $x = 18$ or $x=-2$

Explanation:

Step1: Rewrite in standard form

Move all terms to one side of the equation. Given $x^{2}-6 = 16x + 30$, subtract $16x$ and $30$ from both sides: $x^{2}-16x-6 - 30=0$, which simplifies to $x^{2}-16x - 36=0$.

Step2: Factor the quadratic equation

We need to find two numbers that multiply to $- 36$ and add up to $-16$. The numbers are $-18$ and $2$. So, $x^{2}-16x - 36=(x - 18)(x + 2)=0$.

Step3: Solve for $x$

Set each factor equal to zero. If $x-18 = 0$, then $x = 18$. If $x + 2=0$, then $x=-2$.