Question

-5 - \sqrt{10x + 2} = 5

Explanation:

Step1: Isolate the square root term

Add 5 to both sides of the equation:
$-5 - \sqrt{10x + 2} + 5 = 5 + 5$
Simplify: $-\sqrt{10x + 2} = 10$

Step2: Analyze the square root's nature

The square root $\sqrt{10x + 2}$ is always non - negative (by the definition of the square root function, for any real number $a$, $\sqrt{a}\geq0$ when $a\geq0$). So, $-\sqrt{10x + 2}\leq0$. But in our equation, we have $-\sqrt{10x + 2}=10$, and 10 is positive. A non - positive number cannot equal a positive number.

Answer:

No solution (since the left - hand side $-\sqrt{10x + 2}$ is non - positive and the right - hand side is 10, a positive number, so there is no real value of $x$ that satisfies the equation)