Question

Please solve this radical equation. Show all your steps and explain thoroughly what you did. Thank you for your time and help.

Answer 1

x = 3, x = 4

Explanation:

Given

`√(x-3)` + 3 = x ( subtract 3 from both sides )

`√(x-3)` = x - 3 ( square both sides )

x - 3 = (x - 3)²

x - 3 = x² - 6x + 9 ( subtract x - 3 from both sides )

0 = x² - 7x + 12 ← in standard form

0 = (x - 3)(x - 4) ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

As a check

Substitute these values into the equation and if both sides are equal then they are solutions

x = 3 :
`√(3-3)` + 3 =
`√(0)` + 3 = 3 = 3 = right side

x = 4 :
`√(4-3)` + 3 =
`√(1)` + 3 = 1 + 3 = 4 = right side

solutions are x = 3, x = 4

Answer 2

4,3

Explanation:

Rearrange the equation :

`√(x - 3) = x - 3`

Then, we must square both sides:

x-3 = x²-6x+9

x²-6x+9-x+3=0

x²-7x+12=0

(x-4)(x-3) =0

So x =4,3