Question

Click to see equation, show work pls!

Answer 1

The answer to this equation is 6,9

Answer 2

x = 6, 9

Step 1:

To solve this equation, we need to subtract 3 from both sides like this:

`3√(x-5) +3(-3)=x(-3)\\3√(x-5) =x-3`

Step 2:

We square both sides (multiply using FOIL) to get rid of the radical.

`(3√(x-5) )^2 = (x-3)^2\\(3√(x-5) )^2: 9x-45\\ (x-3)^2: x^2+6x+9\\\\9x-45=x^2-6x+9`

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