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 rearrange the given equation \(x^{2}+2x = 24\) into standard quadratic form \(ax^{2}+bx + c=0\). Subtract 24 from both sides:
\(x^{2}+2x - 24=0\)

Step2: Factor the quadratic

We need to factor \(x^{2}+2x - 24\). We look for 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, the factored form is:
\((x + 6)(x - 4)=0\)

Step3: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).

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

Answer:

4 and -6 (the third option: 4 and -6)