Question

solve for x. separate multiple answers with a comma. x² + 21x + 108 = 0

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(108\) and add up to \(21\). The numbers are \(9\) and \(12\) since \(9\times12 = 108\) and \(9 + 12=21\). So we can factor the quadratic as:
\(x^{2}+21x + 108=(x + 9)(x + 12)=0\)

Step2: Solve for \(x\)

Set each factor equal to zero:
For \(x+9 = 0\), we get \(x=-9\).
For \(x + 12=0\), we get \(x=-12\).

Answer:

\(-12,-9\)