Question

what is $x^2 - 6 = 16x + 30$ rewritten in standard form, then factored?
$(x - 18)(x + 2) = 0$
what value(s) of $x$ make the equation true?
options:
$x = 6$
$x = -18$ or $x = 2$
$x = -6$ or $x = 6$
$x = -2$ or $x = 18$

Explanation:

Step1: Recall zero - product property

If \((a)(b)=0\), then either \(a = 0\) or \(b = 0\). We have the factored form of the equation \((x - 18)(x+2)=0\).

Step2: Solve for \(x\) from each factor

For the factor \(x - 18=0\), we add 18 to both sides of the equation: \(x-18 + 18=0 + 18\), so \(x = 18\).
For the factor \(x + 2=0\), we subtract 2 from both sides of the equation: \(x+2-2=0 - 2\), so \(x=-2\).

Answer:

\(x=-2\) or \(x = 18\) (corresponding to the option: \(x=-2\) or \(x = 18\))