Solve for X in the Quadratic Equation: x² + 16x + 64 = 81

Let's solve the equation $x^2 + 16x + 64 = 81$ step-by-step:

• Step 1: Recognize the Left-Hand Side as a Perfect Square
  Notice that the left-hand side, $x^2 + 16x + 64$, can be factored as $(x + 8)^2$ because $(x + 8)^2 = x^2 + 16x + 64$.
• Step 2: Set the Factored Expression Equal to 81
  We have $(x + 8)^2 = 81$.
• Step 3: Take the Square Root of Both Sides
  Taking the square root on both sides gives two possible equations: $x + 8 = 9$ and $x + 8 = -9$.
• Step 4: Solve Each Equation
  For $x + 8 = 9$:
  Subtract 8 from both sides to get $x = 1$.
  For $x + 8 = -9$:
  Subtract 8 from both sides to get $x = -17$.

Therefore, the solutions to the equation are $x = -17$ or $x = 1$.