Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x² - x = 25

a) 25.75, –24.75
b) 4.97, 5.02
c) 5.52, –4.52
d) 5.45, –4.45

Answer 1

To solve the equation x² - x = 25 by completing the square, move the constant term to the other side, take half of the x coefficient and square it, add the squared term to both sides, simplify the equation, isolate the squared term, take the square root, and round the solutions.

Step-by-step explanation:

To solve the equation x² - x = 25 by completing the square:

1. Move the constant term to the other side to set the equation equal to zero: x² - x - 25 = 0
2. Take half of the coefficient of the x term (-1/2) and square it to get 1/4.
3. Add 1/4 to both sides of the equation to complete the square: x² - x + 1/4 - 25 + 1/4 = 1/4
4. Simplify the equation: (x - 1/2)² - 99/4 = 1/4
5. Isolate the squared term by adding 99/4 to both sides: (x - 1/2)² = 100/4
6. Take the square root of both sides: x - 1/2 = ±√(100/4)
7. Solve for x: x = 1/2 ± √(100/4)
8. Round to the nearest hundredth if necessary: x ≈ 1/2 ± 5
9. Final answer: x ≈ 5.5, -4.5