Question

what is the answer to this radical equation
$\sqrt{x + 13=7}$

Answer 1

Answer:

x = 36

Step-by-step explanation:

Given

$\sqrt{x+13}$ = 7 ( square both sides )

($\sqrt{x+13}$ )² = 7²

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

x = 36

Answer 2

$\sqrt{x+13}=7$

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

$(\sqrt{x+13})^2=7^2$

As defined, $(\sqrt{x})^2 =|x|$

Therefore, $(\sqrt{x+13})^2=|x+13|=x+13$  (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.