We are given the following equation:
[tex]x^2-4x+29=0[/tex]
This an equation of the form:
[tex]ax^2+bx+c=0[/tex]
This solution is given by the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
Replacing the values:
[tex]x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(29)}}{2(1)}[/tex]
Solving the operations:
[tex]x=\frac{4\pm\sqrt[]{16-116}}{2}[/tex][tex]x=\frac{4\pm\sqrt[]{-100}}{2}[/tex]
We have two possible complex solutions:
[tex]\begin{gathered} x=\frac{4\pm10i}{2} \\ \end{gathered}[/tex]
Separating the denominator:
[tex]x=2\pm5i[/tex]
Or in radical form:
[tex]x=2\pm5\sqrt[]{-1}[/tex]
