Question

1. solve $x^{2}+4x - 32 = 0$ for $x$. write all solutions on the same line, separated by commas.

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to - 32 and add up to 4. The numbers are 8 and - 4. So, $x^{2}+4x - 32=(x + 8)(x - 4)=0$.

Step2: Set each factor equal to zero

If $(x + 8)(x - 4)=0$, then $x+8 = 0$ or $x - 4=0$.

Step3: Solve for x

For $x+8 = 0$, we get $x=-8$. For $x - 4=0$, we get $x = 4$.

Answer:

-8,4