Solve the following quadratic equation using square roots: (x+3)2=36

Answer 1

To solve the quadratic equation \((x + 3)^2 = 36\) using square roots, follow these steps:

1. Take the square root of both sides: \[ \sqrt{(x + 3)^2} = \sqrt{36} \] This simplifies to: \[ |x + 3| = 6 \]

2. This absolute value equation gives us two cases to consider:

   • Case 1: \(x + 3 = 6\)
   • Case 2: \(x + 3 = -6\)

3. Solve each case:

   Case 1: \[ x + 3 = 6 \] Subtract 3 from both sides: \[ x = 6 - 3 \] \[ x = 3 \]

   Case 2: \[ x + 3 = -6 \] Subtract 3 from both sides: \[ x = -6 - 3 \] \[ x = -9 \]

Therefore, the solutions to the equation \((x + 3)^2 = 36\) are: \[ x = 3 \quad \text{and} \quad x = -9 \]