Answer:
The solution to the given equation is;
[tex]\begin{gathered} x=3+7i \\ x=3-7i \end{gathered}[/tex]Explanation:
Given the quadratic equation;
[tex]x^2-6x=-58[/tex]Solving the quadratic equation by applying the quadratic formula;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Given the quadratic equation as;
[tex]\begin{gathered} x^2-6x=-58 \\ x^2-6x+58=0 \\ a=1 \\ b=-6 \\ c=58 \end{gathered}[/tex]substituting;
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{6\pm\sqrt[]{(-6)^2-4(1)(58)}}{2(1)} \\ x=\frac{6\pm\sqrt[]{36^{}-4(1)(58)}}{2(1)} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36^{}-232}}{2} \\ x=\frac{6\pm\sqrt[]{-196}}{2} \\ x=\frac{6\pm14i}{2} \\ x=3\pm7i \end{gathered}[/tex]Therefore, the solution to the given equation is;
[tex]\begin{gathered} x=3+7i \\ x=3-7i \end{gathered}[/tex]