Question

Solve the quadratic equation below by completing the square. What are the

solutions?
x^2 + 10x + 22 = 31

A. X=-51 128
B. X-5+ 34
C. X=528
D. *=-51 234

Answer 1

To solve the quadratic equation x^2 + 10x + 22 = 31 by completing the square, follow these steps: Move the constant term to the right side of the equation, combine like terms, complete the square, rewrite as a perfect square, simplifying, take the square root of both sides, isolate x. The solutions are x = -5 + √34 and x = -5 - √34.

Step-by-step explanation:

To solve the quadratic equation x^2 + 10x + 22 = 31 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation: x^2 + 10x + 22 - 31 = 0.
2. Combine like terms: x^2 + 10x - 9 = 0.
3. Complete the square by adding and subtracting the square of half the coefficient of x: x^2 + 10x + 25 - 25 - 9 = 0.
4. Rewrite the equation as a perfect square: (x + 5)^2 - 34 = 0.
5. Simplify: (x + 5)^2 = 34.
6. Take the square root of both sides: x + 5 = ±√34.
7. Isolate x by subtracting 5 from both sides: x = -5 ±√34.

The solutions to the quadratic equation x^2 + 10x + 22 = 31 are x = -5 + √34 and x = -5 - √34.