Question

To solve the quadratic equation x² - 12x - 23 = 0, we need to complete the square.

Answer 1

To solve the quadratic equation x² - 12x - 23 = 0 by completing the square, follow these steps: 1) Take half of the coefficient of x and square it. 2) Add this value inside the parentheses. 3) Simplify and combine like terms. 4) Add the constant term to isolate the squared term. 5) Take the square root of both sides. 6) Solve for x by adding or subtracting the square root value from the constant term.

Step-by-step explanation:

To solve the quadratic equation x² - 12x - 23 = 0, we can complete the square. When completing the square, we want to rewrite the equation in the form (x - h)² = k, where (h,k) represents the coordinates of the vertex of the parabola. Here's how to complete the square:

1. Start by taking half of the coefficient of x, which in this case is -12/2 = -6.
2. Square this value to get (-6)² = 36.
3. Add this value inside the parentheses, so the equation becomes (x - 6)² - 23 - 36 = 0.
4. Simplify and combine like terms to get (x - 6)² - 59 = 0.
5. Add 59 to both sides to isolate the squared term: (x - 6)² = 59.
6. Take the square root of both sides to solve for x - 6: x - 6 = ±√59.
7. Finally, solve for x by adding 6 to both sides: x = 6 ± √59.