Answer
{$-8.10,2.10$}
Work Step by Step
Step 1: Comparing $x^{2}+6x-17=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain:
$a=1$, $b=6$, and $c=-17$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a,b, and c in the formula, we obtain:
$x=\frac{-(6) \pm \sqrt {(6)^{2}-4(1)(-17)}}{2(1)}$
Step 4: $x=\frac{-6 \pm \sqrt {36+68}}{2}$
Step 5: $x=\frac{-6 \pm \sqrt {104}}{2}$
Step 6: $x=\frac{-6 \pm \sqrt {4\times26}}{2}$
Step 7: $x=\frac{-6 \pm 2\sqrt {26}}{2}$
Step 8: $x=-3\pm\sqrt {26}$
Step 9: $x=-3\pm5.099$
Step 10: $x=-3+5.099$ or $x=-3-5.099$
Step 11: $x=2.099\approx2.10$ or $x=-8.099\approx-8.10$
Step 12: Therefore, the solution set is {$-8.10,2.10$}.
