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

Answer 1

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: \[ \boxed{-4 + \sqrt{13}} \quad \text{and} \quad \boxed{-4 - \sqrt{13}} \]