Question

Solve the equation by completing the square.
x^2 - 2 = 9x

Answer 1

1. Rewrite as

x^2 - 9x = 2

Let b = -9

2. add (b/2)^2 to both sides:

x^2 -9x + (-9/2)^2 = -9 + (-9/2)^2
x^2 -9x + 81/4 = -9 + 81/4

3. Re-write the left side as a binomial square:

(x - 9/2)^2 = -9 + 81/4

4. Simplify the right side:
(x - 9/2)^2 = -36/4 + 81/4
(x - 9/2)^2 = (81-36)/4
(x - 9/2)^2 = (45)/4

5. Square root both sides to get

x - 9/2 = + or - sqrt(45/4)

6. Add 9/2 to both sides

x = + or - sqrt(45/4) + 9/2

Answer 2

thanks man!