x^2 − 2 = 9x complete the square

Question

Solve by completing the square.

Answer 1

x² - 2 = 9x.

Subtract 9x from each side.

x² - 2 - 9x = 0

Separate variables and constants aside by adding 2 to each side.

x² - 9x = 2

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

 Here x coefficient = - 9. so, (half the x coefficient)² = (-9/2)²= 81/4.

Add 81/4 to each side.

x² - 9x + 81/4 = 2 +81/4

(x - 9/2)² =8+81/4 = 89/4

(x - 9/2)² = ( ± sqrt (89) /2)²

Take square root both sides.

x - 9/2 = ± sqrt (89) /2

x = 9/2 ± sqrt (89) /2.