Question

What is the answer to this radical equation

`√(x + 13=7)`

Answer 1

x = 36

Explanation:

Given

`√(x+13)` = 7 ( square both sides )

(
`√(x+13)` )² = 7²

x + 13 = 49 ( subtract 13 from both sides )

x = 36

Answer 2

`√(x+13)=7\\`

To solve the radical equation, completing the square all whole equation.

`(√(x+13))^2=7^2\\`

As defined,
`(√(x))^2 =|x|`

Therefore,
`(√(x+13))^2=|x+13|=x+13` (Although Absolute Function gives 2 conditions, however - domain of radical function must be greater than or equal to 0. Meaning x < 0 for another condition doesn't apply.)

`x+13=49\\x=49-13`

Move 13 to subtract.

`x=36`

Therefore, the answer is x = 36.