Respuesta :
The given equation is-
[tex]x^2-10x=-34[/tex]First, we move the independent term to the other side.
[tex]x^2-10x+34=0[/tex]Now, we have to use the quadratic equation to find the solutions.-
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where, a = 1, b = -10, and c = 34.
Replacing these values in the formula, we have.
[tex]\begin{gathered} x_{1,2}=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(1)(34)}}{2(1)} \\ x_{1,2}=\frac{10\pm\sqrt[]{100-136}}{2}=\frac{10\pm\sqrt[]{-36}}{2} \end{gathered}[/tex]But, there's no square root of -36 because it's a negative. To solve this issue, we use complex numbers that way, we would have solutions.
[tex]x_{1,2}=\frac{10\pm\sqrt[]{36}i}{2}=\frac{10\pm6i}{2}=5\pm3i[/tex]