What value is added to both sides of the equation x^2 − 4x = −2

Question

in order to solve by completing the square? 

 

 

Answer 1

The equation is x² - 4x = - 2.

To change the expression (x² - 4x) into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = - 4. so, (half the x coefficient)² = (- 4/2)²= 4.

Add 4 to each side.

x² - 4x + 4 = - 2 + 4

x² - 4x + 4 = 2

Apply Perfect Square Trinomial : a² - 2ab + a² = (a - b)²

(x - 2)² = 2

x - 2 = ± √2

x = ± √2 + 2.

The solutions are 2 + √2 and 2 - √2.