Solve the Quadratic Equation: Find X in (3x+1)^2 + 8 = 12

To solve the equation $(3x + 1)^2 + 8 = 12$, we start by isolating the squared expression:

• First, subtract 8 from both sides to simplify: $(3x + 1)^2 = 12 - 8$.
• This gives $(3x + 1)^2 = 4$.

Next, we take the square root of both sides to remove the square:

• $3x + 1 = \pm 2$, recognizing the positive and negative roots of 4.

We now solve for $x$ in each case:

• Case 1: $3x + 1 = 2$
  Subtract 1 from both sides: $3x = 1$
  Divide by 3: $x = \frac{1}{3}$.
• Case 2: $3x + 1 = -2$
  Subtract 1 from both sides: $3x = -3$
  Divide by 3: $x = -1$.

Therefore, the solutions to the original equation are $x_1 = \frac{1}{3}$ and $x_2 = -1$.