Question

Solve by completing the square:
5x² –10x +2=0

Answer 1

To solve the equation 5x² -10x +2=0 by completing the square, first move the constant term to the other side of the equation. Then, divide the coefficient of x² by 2 and square it. Add the result to both sides of the equation, factor the perfect square, find the square root, and solve for x.

Step-by-step explanation:

To solve the equation 5x² -10x +2=0 by completing the square, follow these steps:

1. Move the constant term to the other side of the equation: 5x² -10x = -2
2. Divide the coefficient of x² by 2 and square it: (10/2)² = 25
3. Add the result from step 2 to both sides of the equation: 5x² -10x +25 = -2 +25
4. Factor the perfect square on the left side: (x - 5)² = 23
5. Take the square root of both sides: x - 5 = ±√23
6. Add 5 to both sides: x = 5 ± √23