Question

for what values of x is $x^2 + 2x = 24$ true?
○ $-6$ and $-4$
○ $-4$ and $6$
○ $4$ and $-6$
○ $6$ and $4$

Explanation:

Step1: Rearrange the equation

First, we rewrite the equation \(x^{2}+2x = 24\) in standard quadratic form \(ax^{2}+bx + c=0\) by subtracting 24 from both sides:
\(x^{2}+2x - 24=0\)

Step2: Factor the quadratic

We need to find two numbers that multiply to \(- 24\) and add up to \(2\). The numbers are \(6\) and \(-4\) because \(6\times(-4)=-24\) and \(6+( - 4)=2\).
So, we can factor the quadratic as:
\((x + 6)(x-4)=0\)

Step3: Solve for x

Using the zero - product property, if \((x + 6)(x - 4)=0\), then either \(x+6 = 0\) or \(x - 4=0\).

• If \(x+6=0\), then \(x=-6\).
• If \(x - 4=0\), then \(x = 4\).

Answer:

C. 4 and -6