Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation?

Question

{–11, 3}
{–3, 11}
{–4, 4}
{–7, 7}

Answer 1

To solve the equation \( x^2 + 8x = 33 \) by completing the square, we will follow these steps:

1. Move the constant term to the right side: \[ x^2 + 8x - 33 = 0 \]

2. To complete the square, take the coefficient of \( x \) (which is 8), divide it by 2, and square it. This gives us: \[ \left( \frac{8}{2} \right)^2 = 4^2 = 16 \]

3. Add and subtract this square on the left side of the equation: \[ x^2 + 8x + 16 - 16 - 33 = 0 \] Simplifying this, we have: \[ (x + 4)^2 - 49 = 0 \]

4. Move the constant term to the right side: \[ (x + 4)^2 = 49 \]

5. Take the square root of both sides: \[ x + 4 = \pm 7 \]

6. Solve for \( x \):

   • First case: \[ x + 4 = 7 \quad \Rightarrow \quad x = 7 - 4 \quad \Rightarrow \quad x = 3 \]
   • Second case: \[ x + 4 = -7 \quad \Rightarrow \quad x = -7 - 4 \quad \Rightarrow \quad x = -11 \]

Thus, the solution set of the equation is \( { -11, 3 } \).

Therefore, the correct answer is: \[ { -11, 3 } \]