Question

How do u solve this:
Square root of 6x-9 equals x

Answer 1

√6x-9=x
6x-9=x²
x²-6x+9=0
(x-3)(x-3)=0
x=3
check
√6*3-9=3
√18-9=3
√9=3
3=3

Answer 2

`√(6x-9) = x`

first we are going to get rid of the square root by raising both sides to the power of 2

6x - 9 = x²
x² - 6x + 9 = 0

now the equation is a quadratic, and you can solve for x

i'm going to factor it, but there are many ways to solve for a quadratic
(x - 3)(x - 3) = 0
If you FOIL this, it becomes x² - 6x + 9

(x - 3)² = 0
x - 3 = 0
x = 3

to check the answer, you can plug 3 back into the original equation


`√(6(3) - 9) = 3`

`√(18 - 9) = 3`

`√(9) = 3`

`3 = 3`