Solve the equation for $x$ :
\[
x^{2}+17 x+60=0
\]

Answer

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Answer

$\boxed{x = -5, -12}$

Steps

Step 1 ：Given the quadratic equation: $x^2 + 17x + 60 = 0$

Step 2 ：Using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 1$, $b = 17$, and $c = 60$

Step 3 ：Calculate the discriminant: $\Delta = b^2 - 4ac = 49$

Step 4 ：Find the two solutions: $x_1 = \frac{-17 + \sqrt{49}}{2} = -5$ and $x_2 = \frac{-17 - \sqrt{49}}{2} = -12$

Step 5 ：$\boxed{x = -5, -12}$