College Algebra, Chapter 1, 1.1, Section 1.1, Problem 58

The equation $6x^2 + 100 = 0$ involves a power of the variable. Find all real solutions of the equation.

$
\begin{equation}
\begin{aligned}
6x^2 + 100 &= 0 && \text{Subtract both sides by 100}\\
\\
6x^2 + 100 - 100 &= 0 - 100 && \text{Simplify}\\
\\
6x^2 &= -100 && \text{Divide both sides by 6}\\
\\
\frac{\cancel{6}x^2}{\cancel{6}} &= \frac{-100}{6} && \text{Simplify and reduce to lowest term}\\
\\
x^2 &= \frac{-50}{3} && \text{Take the square root of both sides}\\
\\
\sqrt{x^2} &= \pm \sqrt{\frac{-50}{3}} && \text{Simplify}\\
\\
x &= \pm \sqrt{\frac{-50}{3}}
\end{aligned}
\end{equation}
$


The equation $6x^2 + 100 = 0$ has no real solution because $\displaystyle x = \pm \sqrt{\frac{-50}{3}}$ does not exist.