Question

Solve x2 + 2x =1 for x by completing the square.

Answer 1

To solve the equation x^2 + 2x = 1, we complete the square by adding the square of half the coefficient of x to both sides, factor the perfect square, take the square root of both sides, and solve for x, resulting in x = -1 ± √2.

Step-by-step explanation:

To solve the equation x^2 + 2x = 1 by completing the square, we follow these steps:

1. First, we move the constant term to the right side to get x^2 + 2x - 1 = 0.
2. Next, we add the square of half the coefficient of x to both sides to complete the square. The coefficient of x is 2, so we add (2/2)^2 which is 1 to both sides yielding x^2 + 2x + 1 = 2.
3. Now, the left side is a perfect square, (x + 1)^2, so the equation becomes (x + 1)^2 = 2.
4. Then, we take the square root of both sides, giving x + 1 = ±√2.
5. Finally, we solve for x by subtracting 1 from both sides to get x = -1 ± √2.

This gives us the two solutions for x in the original equation.