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

Answer

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Answer

$x = - 5, - 12$

Steps

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

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

Step 3 ：Calculate the discriminant: $Δ = b^{2} - 4 a c = 49$

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 ： $x = - 5, - 12$