Question

solve the quadratic equation x^2 + 8x - 29 = 0 using the quadratic formula. give simplified exact answers.

Answer 1

Given the Quadratic Equation:

`x^2+8x-29=0`

You can identify that it has this form:

`ax^2+bx+c=0`

The Quadratic Formula is:

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

In this case:

`\begin{gathered} a=1 \\ b=8 \\ c=-29 \end{gathered}`

Then, you can substitute values into the Quadratic Formula and simplify:

`\begin{gathered} x=\frac{-(8)\pm\sqrt[]{(8)^2-(4)(1)(-29)}}{2\cdot1} \\ \\ x=\frac{-8\pm\sqrt[]{180}}{2} \end{gathered}`

Notice that the symbol ± indicates that you actually have these two equations:

`\begin{gathered} x_1=\frac{-8+\sqrt[]{180}}{2} \\ \\ \\ x_2=\frac{-8-\sqrt[]{180}}{2} \end{gathered}`

Therefore, evaluating, you get:

`\begin{gathered} x_1=-4+3\sqrt[]{5} \\ \\ x_2=-4-3\sqrt[]{5} \end{gathered}`

Hence, the answer is:

`\begin{gathered} x_1=-4+3\sqrt[]{5} \\ \\ x_2=-4-3\sqrt[]{5} \end{gathered}`