Question

Solve the quadratic equation x²-12x+23=0by completing the square.

a) x= 13-√6
b) x= -6±√13
c) x= 13±√6
d) x= 6±√13

Answer 1

To solve the quadratic equation x²-12x+23=0 by completing the square, transform it into a perfect square equation, (x-6)²=13, and solve for x to find the answer to be x = 6±√13.

Step-by-step explanation:

To solve the quadratic equation x²-12x+23=0 by completing the square, follow these steps:

1. Rewrite the equation in the form of x² - 12x = -23.
2. Divide the coefficient of x, which is -12, by 2 to get -6 and then square it to get 36.
3. Add 36 to both sides of the equation to form a perfect square on the left side. The equation becomes x² - 12x + 36 = 13.
4. This can be factored into (x-6)² = 13.
5. Take the square root of both sides to get x - 6 = ±√13.
6. Add 6 to both sides of the equation to solve for x, resulting in x = 6 ± √13.

Therefore, the correct answer is d) x = 6±√13.