Respuesta :
Given the Quadratic Equation:
[tex]x^2+8x-29=0[/tex]You can identify that it has this form:
[tex]ax^2+bx+c=0[/tex]The Quadratic Formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case:
[tex]\begin{gathered} a=1 \\ b=8 \\ c=-29 \end{gathered}[/tex]Then, you can substitute values into the Quadratic Formula and simplify:
[tex]\begin{gathered} x=\frac{-(8)\pm\sqrt[]{(8)^2-(4)(1)(-29)}}{2\cdot1} \\ \\ x=\frac{-8\pm\sqrt[]{180}}{2} \end{gathered}[/tex]Notice that the symbol ± indicates that you actually have these two equations:
[tex]\begin{gathered} x_1=\frac{-8+\sqrt[]{180}}{2} \\ \\ \\ x_2=\frac{-8-\sqrt[]{180}}{2} \end{gathered}[/tex]Therefore, evaluating, you get:
[tex]\begin{gathered} x_1=-4+3\sqrt[]{5} \\ \\ x_2=-4-3\sqrt[]{5} \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{gathered} x_1=-4+3\sqrt[]{5} \\ \\ x_2=-4-3\sqrt[]{5} \end{gathered}[/tex]