Question

Solve for x. Express your answers in simplest radical form. x^2-4x+29=0

Answer 1

We are given the following equation:

`x^2-4x+29=0`

This an equation of the form:

`ax^2+bx+c=0`

This solution is given by the quadratic formula:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Replacing the values:

`x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(29)}}{2(1)}`

Solving the operations:

`x=\frac{4\pm\sqrt[]{16-116}}{2}`
`x=\frac{4\pm\sqrt[]{-100}}{2}`

We have two possible complex solutions:

`\begin{gathered} x=(4\pm10i)/(2) \\ \end{gathered}`

Separating the denominator:

`x=2\pm5i`

Or in radical form:

`x=2\pm5\sqrt[]{-1}`