Question

1. solve for the two possible values of x:

4x² + 32x = 0

write all solutions on the same line separated by commas.

enter your next step here

Explanation:

Step1: Factor out 4x

We can factor out the greatest common factor, which is \(4x\), from the left - hand side of the equation \(4x^{2}+32x = 0\). Using the distributive property \(ab + ac=a(b + c)\), where \(a = 4x\), \(b=x\) and \(c = 8\), we get:
\(4x(x + 8)=0\)

Step2: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). So, for the equation \(4x(x + 8)=0\), we have two cases:
Case 1: \(4x=0\)
Divide both sides of the equation \(4x = 0\) by 4. We get \(x=\frac{0}{4}=0\).
Case 2: \(x + 8=0\)
Subtract 8 from both sides of the equation \(x + 8=0\). We get \(x=-8\).

Answer:

\(0,-8\)