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.