EXPLANATION
Given the equation 10m^2 - 11m + 4 = 0
We can see that this is a quadratic equation so we need to apply the quadratic formula as shown as follows:
[tex]m_{1,2}=\frac{-(-11)\pm\sqrt[]{(-11)^2-4\cdot10\cdot4}}{2\cdot10}[/tex]Simplifying:
[tex]m_{1,2}=\frac{11\pm\sqrt[]{121-160}}{20}[/tex][tex]m_{1,2}=\frac{11\pm\sqrt[]{-39}}{20}[/tex]Separate the solutions:
[tex]m_1=\frac{11+\sqrt[]{39}i}{20}[/tex][tex]m_2=\frac{11-\sqrt[]{39}i}{20}[/tex]Rewritting the expressions:
[tex]m_1=\frac{11}{20}+\frac{\sqrt[]{39}i}{20}[/tex][tex]m_2=\frac{11}{20}-\frac{\sqrt[]{39}i}{20}[/tex]The solutions to the quadratic equations are:
[tex]m_{}=\frac{11}{20}+i\frac{\sqrt[]{39}}{20}[/tex][tex]m=\frac{11}{20}-i\frac{\sqrt[]{39}}{20}[/tex]