Answer:
x = 6, 9
Step 1:
To solve this equation, we need to subtract 3 from both sides like this:
[tex]3\sqrt{x-5} +3(-3)=x(-3)\\3\sqrt{x-5} =x-3[/tex]
Step 2:
We square both sides (multiply using FOIL) to get rid of the radical.
[tex](3\sqrt{x-5} )^2 = (x-3)^2\\(3\sqrt{x-5} )^2: 9x-45\\ (x-3)^2: x^2+6x+9\\\\9x-45=x^2-6x+9[/tex]
If you did not understand how these were done, here is an example:
(x + 1)(x + 2)
First terms: x * x = x^2
Outer terms: x * 2 = 2x
Inner terms: 1 * x = x
2x - x = x
Last terms: 1 * 2 = 2
x^2 + x + 2
Step 3:
Solve for x:
9x - 45 = x^2 - 6x + 9
x^2 - 6x + 9 (+45) = 9x - 45 (+45)
x^2 - 6x + 54 (-9x) = 9x (-9x)
x^2 - 15x + 54 = 0
Factor:
(x^2 - 6x) + (- 9x + 54)
x(x - 6) - 9(x - 6)
Factor out (x - 6):
(x - 6)(x - 9) = 0
x - 6 = 0; 6 - 6 = 0
x - 9 = 0; 9 - 9 = 0
Our anwer: x = 6, 9
