Question

solve $x^2 + 2x + 5 = 4$ by completing the square. select the solution(s).
$x = -4$ $x = -3$ $x = -2$ $x = -1$ $x = 0$
$x = 1$ $x = 2$ $x = 3$ $x = 4$ no solutions

Explanation:

Step1: Isolate the constant term

Subtract 4 from both sides: $x^2 + 2x + 5 - 4 = 0$ → $x^2 + 2x + 1 = 0$

Step2: Complete the square

The coefficient of $x$ is 2, half of it is 1, square of 1 is 1. The left side is already a perfect square: $(x + 1)^2 = 0$

Step3: Solve for x

Take square root: $x + 1 = 0$ → $x = -1$

Answer:

\( x = -1 \)