Question

Solve the quadratic equations by completing the square.
x^2-4x=-1

Answer 1

2 ± √3

Explanation:

Solving quadratic equation by completing squares:

x² - 4x = -1

• Divide the coefficient of x by 2.

4 ÷ 2 = 2

• Now, square the result and add that to both sides of the equation.

2² = 2* 2 = 4

x² - 4x + 4 = -1 + 4

x² - 4x + 4 = 3

x² - 2 * x * 2 + 2² = 3

• Compare it with a² - 2ab + b² . Now , a = x and b = 2

(x - 2)² = 3

• Take square root both sides

x - 2 = ±√3

x = 2 ± √3

Solutions: x = 2 +√3 ; 2 - √3