Question

Solve for x for this problem

Answer 1

x = 5 and 6

Explanation:

1. Square both sides
x - 5 = (x - 5)(x - 5)
2. Simplify the right side
x - 5 = x^2 - 10x + 25
3. Add 5 to both sides
x = x^2 - 10x + 30
4. Subtract x from both sides
0 = x^2 - 11x + 30
5. Factor
0 = (x-5)(x-6)
x = 5,6

Answer 2

x = 5 , x = 6

Explanation:

`√(x-5)` = x - 5 ( square both sides )

x - 5 = (x - 5)² ← expand using FOIL

x - 5 = x² - 10x + 25 ← subtract x - 5 from both sides

0 = x² - 11x + 30 ← in standard form

0 = (x - 5)(x - 6) ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x - 6 = 0 ⇒ x = 6

As a check

substitute these values into the equation and if both sides are equal then these values are the solutions.

x = 5

left side =
`√(5-5)` =
`√(0)` = 0

right side = 5 - 5 = 0

then x = 5 is a solution

----------------------------------

x = 6

left side =
`√(6-5)` =
`√(1)` = 1

right side = 6 - 5 = 1

then x = 6 is a solution