Question
Solve the following quadratic equation for all values of xx in simplest form. 3, left parenthesis, x, plus, 4, right parenthesis, squared, equals, 39 3(x+4) 2 = 39
Answers
GPT-4o mini
To solve the quadratic equation \( 3(x + 4)^2 = 39 \), we can follow these steps:
1. **Divide both sides by 3**:
\[
(x + 4)^2 = \frac{39}{3} \Rightarrow (x + 4)^2 = 13
\]
2. **Take the square root of both sides**:
\[
x + 4 = \pm \sqrt{13}
\]
3. **Isolate \( x \)**:
\[
x = -4 \pm \sqrt{13}
\]
This gives us two solutions:
\[
x = -4 + \sqrt{13} \quad \text{and} \quad x = -4 - \sqrt{13}
\]
Thus, the solutions in simplest form are:
\[
\boxed{-4 + \sqrt{13}} \quad \text{and} \quad \boxed{-4 - \sqrt{13}}
\]
1. **Divide both sides by 3**:
\[
(x + 4)^2 = \frac{39}{3} \Rightarrow (x + 4)^2 = 13
\]
2. **Take the square root of both sides**:
\[
x + 4 = \pm \sqrt{13}
\]
3. **Isolate \( x \)**:
\[
x = -4 \pm \sqrt{13}
\]
This gives us two solutions:
\[
x = -4 + \sqrt{13} \quad \text{and} \quad x = -4 - \sqrt{13}
\]
Thus, the solutions in simplest form are:
\[
\boxed{-4 + \sqrt{13}} \quad \text{and} \quad \boxed{-4 - \sqrt{13}}
\]