Question

choose an action to perform.$x^2 - 4x - 45 = 0$ways to rewrite expressionsapply exponentdistributefactor common factorreverse multiplicationrewrite signscombine like termseliminate radicalfactor quadraticrewrite fractionsequation transformationsadd to both sidessubtract from both sidesmultiply both sidesdivide both sidesapply quadratic formulaother actionsapply zero product propertyseparate roots

Explanation:

Step1: Factor the quadratic expression

We need two numbers that multiply to $-45$ and add to $-4$. These numbers are $-9$ and $5$.
$x^2 - 4x - 45 = (x - 9)(x + 5) = 0$

Step2: Apply Zero Product Property

Set each factor equal to 0.
$x - 9 = 0$ or $x + 5 = 0$

Step3: Solve for $x$

Solve each linear equation.
$x = 9$ or $x = -5$

Answer:

$x = 9$ or $x = -5$