Question

Solve x²−4x+1=0 by completing square method.

Answer 1

To solve the quadratic equation x^2-4x+1=0 by completing the square, we find the number to add to both sides, creating a perfect square trinomial. After adding, we take the square root of both sides and solve for x, yielding the solution x = 2 ± √3.

Step-by-step explanation:

To solve the quadratic equation x²-4x+1=0 by completing the square method, follow these steps:

1. Rearrange the equation and move the constant term to the other side: x²-4x = -1.
2. Divide the coefficient of x (which is -4) by 2, and then square it to find the value to be added to both sides of the equation to complete the square: (-4/2)² = 4.
3. Add this value to both sides: x²-4x + 4 = -1 + 4, which simplifies to (x-2)² = 3.
4. Take the square root of both sides: x-2 = ±√3.
5. Add the value used to complete the square (2) to both sides of the equation to solve for x: x = 2 ± √3.

Therefore, the solution to the equation by completing the square is x = 2 ± √3.