Answer
The solution to the quadratic equation is
[tex]x=1\pm3i[/tex]
EXPLANATION
Problem Statement
The question gives us the beginning of the application of the Quadratic formula on a quadratic equation. We are required to simplify the expression and get in more certain terms, the values of x.
The expression given is:
[tex]\begin{gathered} x^2-2x+10=0 \\ \\ x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \end{gathered}[/tex]
Solution
Let us begin to simplify the expression below:
[tex]\begin{gathered} x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \\ \\ x=\frac{2\pm\sqrt[]{(-2\times-2)^{}-(4\times1\times10)}}{2} \\ \\ x=\frac{2\pm\sqrt[]{4-40}_{}}{2} \\ \\ x=\frac{2\pm\sqrt[]{-36}}{2} \\ \\ \text{From the laws of indices, we have:} \\ \sqrt[]{a\times b}=\sqrt[]{a}\times\sqrt[]{b} \\ \\ x=\frac{2\pm\sqrt[]{-1\times36}}{2} \\ \\ x=\frac{2\pm(\sqrt[]{-1})(\sqrt[]{36})}{2} \\ \\ \text{ We know that, } \\ \sqrt[]{-1}=i \\ \\ x=\frac{2\pm(i)(6)}{2} \\ \\ x=\frac{2\pm6i}{2} \\ \\ x=\frac{2(1\pm3i)}{2} \\ \\ 2\text{ Crosses out} \\ \\ x=1\pm3i \end{gathered}[/tex]
Final Answer
The solution to the quadratic equation is
[tex]x=1\pm3i[/tex]
