Question

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

Answer 1

Answer:

2 ± √3

Step-by-step 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