Question

Solve the quadratic equation x²−6x−59=0 by completing the square.

a. x=−3±2
b. x=−3±
c. x=−2±3
d. x=3±2

Answer 1

To solve the quadratic equation by completing the square, we need to follow these steps: move the constant term, take half of the x term coefficient and square it, add the square to both sides, simplify, and take the square root. The solution is x = 3 ± √68.

Step-by-step explanation:

To solve the quadratic equation x² - 6x - 59 = 0 by completing the square, follow these steps:

1. Move the constant term (-59) to the right side of the equation: x² - 6x = 59.
2. Take half of the coefficient of the x term and square it: (6/2)² = 9.
3. Add the square from step 2 to both sides of the equation: x² - 6x + 9 = 59 + 9.
4. Simplify the equation: (x - 3)² = 68.
5. Take the square root of both sides of the equation: x - 3 = ±√68.
6. Add 3 to both sides of the equation: x = 3 ± √68.

Therefore, the correct answer is option d. x = 3 ± 2.