check your solution.\n2. $sqrt{x + 25}=2$

Answer:

$x = - 21$

Explanation:

Step1: Isolate the square - root term

The equation is $\sqrt{x + 25}=2$. Since the square - root is already isolated on the left - hand side.

Step2: Square both sides

Squaring both sides gives $(\sqrt{x + 25})^2=2^2$. By the property $(\sqrt{a})^2=a$ (for $a\geq0$), we have $x + 25=4$.

Step3: Solve for $x$

Subtract 25 from both sides: $x=4 - 25$. So, $x=-21$.

Step4: Check the solution

Substitute $x = - 21$ into the original equation: $\sqrt{-21 + 25}=\sqrt{4}=2$. The left - hand side equals the right - hand side, so $x=-21$ is the solution.