Question

How do I solve this problem and check all the solutions?

Answer 1

x = 10

Explanation:

Given

x -
`√(2x+5)` = 5 ( subtract x from both sides )

-
`√(2x+5)` = 5 - x ( divide all terms by - 1 )

`√(2x+5)` = x - 5 ( square both sides )

2x + 5 = (x - 5)²

2x + 5 = x² - 10x + 25 ( subtract 2x + 5 from both sides )

0 = x² - 12x + 20 ← in standard form

0 = (x - 2)(x - 10) ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 10 = 0 ⇒ x = 10

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions

x = 2

2 -
`√(4+5)` = 2 -
`√(9)` = 2 - 3 = - 1 ≠ 5

Thus x = 2 is an extraneous solution

x = 10

10 -
`√(20+5)` = 10 -
`√(25)` = 10 - 5 = 5 = right side

Thus x = 10 is the solution

Answer 2

x-5=sqrt(2x+5)

then square both sides

x2-10x+25=2x+5

x2-8x+20=0

rest is trivial

Explanation: