# How to Solve Power Equations

Power equations, or quadratic equations without a first degree term, are super fun to solve. You need to have control of roots to be able to find the answer without any aids. You also need to have control of the change side, change sign rule and isolating variables.

Rule

### PowerEquations

$\begin{array}{llll}\hfill a{x}^{2}+b& =0\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill x& =±\sqrt{-\frac{b}{a}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 1

$\begin{array}{llll}\hfill {x}^{2}& =49\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \sqrt{{x}^{2}}& =\sqrt{49}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill x& =±7\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 2

$\begin{array}{llll}\hfill 2{x}^{2}& =98\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{2{x}^{2}}{2}& =\frac{98}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill {x}^{2}& =49\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \sqrt{{x}^{2}}& =\sqrt{49}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill x& =±7\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Think About This

### The Root of a Negative Number

Why do you think we can’t get the square root of a negative number?

Any square root is calculated such that $\sqrt{{a}^{2}}=a$. Any number raised to the power of 2 always becomes a positive number, since $-×-=+$. This means that ${a}^{2}>0$, even if $a<0$.

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