Answer
The solution of the equation ${{x}^{2}}-6x+10=0$ in standard form is $\left\{ 3+i,3-i \right\}$.
Work Step by Step
Consider the equation, ${{x}^{2}}-6x+10=0$
Compare the equation ${{x}^{2}}-6x+10=0$ with $a{{x}^{2}}+bx+c$.
$\begin{align}
& a=1 \\
& b=-6 \\
& c=10
\end{align}$
Substitute $a=1$, $b=-6$ and $c=10$ in the formula $x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.
$\begin{align}
& x=\frac{-\left( -6 \right)\pm \sqrt{{{\left( -6 \right)}^{2}}-4\left( 1 \right)\left( 10 \right)}}{2\left( 1 \right)} \\
& =\frac{6\pm \sqrt{36-40}}{2} \\
& =\frac{6\pm \sqrt{-4}}{2}
\end{align}$
Use the property $\sqrt{-b}=i\sqrt{b}$.
\[\begin{align}
& x=\frac{6\pm i\sqrt{4}}{2} \\
& =\frac{6\pm 2i}{2} \\
& =\frac{6}{2}\pm \frac{2}{2}i \\
& =3\pm i
\end{align}\]
Therefore, the solution of the equation ${{x}^{2}}-6x+10=0$ in standard form is $\left\{ 3+i,3-i \right\}$.
