Solve the following quadratic equation for all values of xx in simplest form.

Question

5, left parenthesis, x, plus, 3, right parenthesis, squared, minus, 3, equals, 42
5(x+3)
2
−3=
42

Answer 1

To solve the equation \( 5(x + 3)^2 - 3 = 42 \), we will follow these steps:

1. Isolate the quadratic term: \[ 5(x + 3)^2 - 3 = 42 \] Add 3 to both sides: \[ 5(x + 3)^2 = 45 \]

2. Divide by 5: \[ (x + 3)^2 = 9 \]

3. Take the square root: Taking the square root of both sides gives us two equations: \[ x + 3 = 3 \quad \text{or} \quad x + 3 = -3 \]

4. Solve for \( x \):

   • For \( x + 3 = 3 \): \[ x = 3 - 3 = 0 \]
   • For \( x + 3 = -3 \): \[ x = -3 - 3 = -6 \]

5. Final Solutions: The solutions for the quadratic equation are: \[ x = 0 \quad \text{and} \quad x = -6 \]

Thus, the values of \( x \) in simplest form are \( \boxed{0} \) and \( \boxed{-6} \).