To solve the equation x² + 4x - 11 = 0 by completing the square, follow these steps:
1. Identify the coefficients of x² and x. In this equation, a = 1 (coefficient of x²) and b = 4 (coefficient of x).
2. Move the constant term (-11 in this case) to the other side of the equation by adding it to both sides:
x² + 4x = 11
3. To complete the square, take half of the coefficient of x (which is b/2) and square it. In this case, b/2 = 4/2 = 2. Squaring 2 gives 4.
4. Add and subtract the squared value (4) inside the parentheses on the left side of the equation:
x² + 4x + 4 - 4 = 11
5. Factor the trinomial (x² + 4x + 4) as a square of a binomial:
(x + 2)² - 4 = 11
6. Simplify the equation:
(x + 2)² = 15
7. To solve for x, take the square root of both sides:
x + 2 = ±√15
8. Solve for x by subtracting 2 from both sides:
x = -2 ±√15
Therefore, the solutions to the equation x² + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.
