Question

solve the equation by using the quadratic formula.
$n^2 + 4n - 60 = 0$

the solution set is ${ square }$.

Explanation:

Step1: Identify coefficients

For $n^2 + 4n - 60 = 0$, $a=1$, $b=4$, $c=-60$

Step2: Recall quadratic formula

$$n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Step3: Compute discriminant

$\Delta = b^2 - 4ac = 4^2 - 4(1)(-60) = 16 + 240 = 256$

Step4: Substitute into formula

$$n = \frac{-4 \pm \sqrt{256}}{2(1)} = \frac{-4 \pm 16}{2}$$

Step5: Calculate two solutions

First solution: $n = \frac{-4 + 16}{2} = \frac{12}{2} = 6$
Second solution: $n = \frac{-4 - 16}{2} = \frac{-20}{2} = -10$

Answer:

$\{6, -10\}$