x^2-18x=-56

Question

solve the equation by completing the square.

Answer 1

The equation is x² - 18x = - 56.

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

 Here x coefficient = - 18. so, (half the x coefficient)² = (- 18/2)²= 81.

Add 81 to each side.

x² - 18x + 81 = - 56 + 81

(x - 9)² = 25

(x - 9)² = (± 5)²

x - 9 = ± 5

x = 9 + 5 and x = 9 - 5

x = 14 and x = 4.

The solutions are x = 14 and x = 4.