Answer :
[tex] \sqrt{6x-9} = x[/tex]
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
[tex] \sqrt{6(3) - 9} = 3 [/tex]
[tex] \sqrt{18 - 9} = 3[/tex]
[tex] \sqrt{9} = 3[/tex]
[tex]3 = 3[/tex]
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
[tex] \sqrt{6(3) - 9} = 3 [/tex]
[tex] \sqrt{18 - 9} = 3[/tex]
[tex] \sqrt{9} = 3[/tex]
[tex]3 = 3[/tex]
