Complete the square to solve the following quadratic equation x squared + 2x - 8 = 0

Answer 1

To solve the quadratic equation \( x^2 + 2x - 8 = 0 \) by completing the square, follow these steps:

1. Move the constant term to the other side of the equation:

   \[ x^2 + 2x = 8 \]

2. Complete the square on the left side. To do this, take half of the coefficient of \( x \) (which is 2), square it, and add it to both sides. Half of 2 is 1, and \( 1^2 = 1 \).

   \[ x^2 + 2x + 1 = 8 + 1 \]

   This simplifies to:

   \[ x^2 + 2x + 1 = 9 \]

3. Rewrite the left side as a squared binomial:

   \[ (x + 1)^2 = 9 \]

4. Take the square root of both sides:

   \[ x + 1 = \pm 3 \]

5. Solve for \( x \) by isolating it:

   • For the positive case: \[ x + 1 = 3 \implies x = 3 - 1 = 2 \]

   • For the negative case: \[ x + 1 = -3 \implies x = -3 - 1 = -4 \]

Thus, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are:

\[ x = 2 \quad \text{and} \quad x = -4 \]