Radical or Exponents or Power is defined as the number of times that a variable or constant is being repeated. It is also called power raised. Exponents are used to describing number of times in a single notation

The radical equation given to us

\(\displaystyle{6}=\sqrt{{{x}^{{2}}-{2}{x}+{12}}}\)

To find the solution for the given radical equation

Solution to the question

We have,

\(\displaystyle{6}=\sqrt{{{x}^{{2}}-{2}{x}+{12}}}\)

Squaring both sides we obtain,

\(\displaystyle{6}^{{2}}={\left(\sqrt{{{x}^{{2}}-{2}{x}+{12}}}\right)}^{{2}}\)

\(\displaystyle{36}={x}^{{2}}-{2}{x}+{12}\)

\(\displaystyle{x}^{{2}}-{2}{x}+{12}-{36}={0}\)

\(\displaystyle{x}^{{2}}-{2}{x}-{24}={0}\)

\(\displaystyle{x}^{{2}}-{6}{x}+{4}{x}={0}\)

\(\displaystyle{x}{\left({x}-{6}\right)}+{4}{\left({x}-{6}\right)}={0}\)

\(\displaystyle{\left({x}+{4}\right)}{\left({x}-{6}\right)}={0}\)

either \(x=-4\ \text{or}\ x=6\)

There are two valid solutions \(\displaystyle{x}=-{4}{\quad\text{and}\quad}{x}={6}\)