Question

what is the solution of \\(\sqrt{x - 4} + 5 = 2\\)?\
\\(\bigcirc\\) \\(x = -17\\)\
\\(\bigcirc\\) \\(x = 13\\)\
\\(\bigcirc\\) \\(x = 53\\)\
\\(\bigcirc\\) no solution

Explanation:

Step1: Isolate the square root term

Subtract 5 from both sides of the equation $\sqrt{x - 4}+5 = 2$.
$\sqrt{x - 4}=2 - 5$
$\sqrt{x - 4}=-3$

Step2: Analyze the square root function

The square root of a real number, $\sqrt{a}$, is defined such that $\sqrt{a}\geq0$ for all real numbers $a\geq0$. Here, the left - hand side $\sqrt{x - 4}$ represents a square root, so it must be non - negative. But the right - hand side is - 3, which is negative. Since a non - negative number cannot be equal to a negative number, there is no real number $x$ that satisfies the equation.

Answer:

no solution