Question

solve $x^{2}+3x - 88 = 0$ for $x$. write all solutions on the same line, separated by commas.

Explanation:

Step1: Factor the quadratic equation

We find two numbers that multiply to $-88$ and add to $3$: $11$ and $-8$.
$x^2 + 3x - 88 = (x + 11)(x - 8) = 0$

Step2: Set each factor to zero

For the product to be zero, each factor can be zero.
$x + 11 = 0$ or $x - 8 = 0$

Step3: Solve for $x$

Solve each linear equation separately.
$x = -11$ or $x = 8$

Answer:

$-11, 8$