Question

Solve for x for this problem

Answer 1

Answer:

x = 5 and 6

Step-by-step 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

Answer:

x = 5 , x = 6

Step-by-step explanation:

$\sqrt{x-5}$ = 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 = $\sqrt{5-5}$ = $\sqrt{0}$ = 0

right side = 5 - 5 = 0

then x = 5 is a solution

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x = 6

left side = $\sqrt{6-5}$ = $\sqrt{1}$ = 1

right side = 6 - 5 = 1

then x = 6 is a solution