Question

solve the radical equation. check your solution(s). write
o solution\ if there is no solution.\\(\sqrt{-1 - x} - 10 = -9\\)\\(x = \square\\)

Explanation:

Step1: Isolate the radical term

Add 10 to both sides of the equation $\sqrt{-1 - x}-10=-9$:
$\sqrt{-1 - x}-10 + 10=-9 + 10$
$\sqrt{-1 - x}=1$

Step2: Eliminate the radical

Square both sides of the equation $\sqrt{-1 - x}=1$:
$(\sqrt{-1 - x})^2=1^2$
$-1 - x = 1$

Step3: Solve for x

Add 1 to both sides:
$-1 - x+1 = 1 + 1$
$-x = 2$
Multiply both sides by -1:
$x=-2$

Step4: Check the solution

Substitute $x = -2$ into the original equation:
Left - hand side: $\sqrt{-1-(-2)}-10=\sqrt{-1 + 2}-10=\sqrt{1}-10 = 1-10=-9$
Right - hand side: $-9$
Since the left - hand side equals the right - hand side, $x=-2$ is a valid solution.

Answer:

-2