Question

In the following exercises, solve by using the Quadratic Formula:$q^2+3q-18=0$

Short answer

The solution of the quadratic equation is$q=3$and$q=-6$

Step-by-step solution

Given information

We are given a quadratic equation$q^2+3q-18=0$

Identify the values of a,b,c

On comparing with standard equation we get$a=1,b=3,c=-18$

Write the quadratic formula and substitute the values in it

The quadratic formula can be given as

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

On substituting the values we get

$q=\frac{-3\pm \sqrt{9-4\left(1\right)(-18)}}{2\left(1\right)}$

Simplify

On simplifying we get

$$\begin{gathered} q=\frac{-3\pm \sqrt{9+72}}{2} \\ q=\frac{-3\pm \sqrt{81}}{2} \\ q=\frac{-3\pm 9}{2} \end{gathered}$$

On further simplifying we get

$$\begin{gathered} q=\frac{-3+9}{2} \\ q=\frac{6}{2} \\ q=3 \end{gathered}$$and$$\begin{gathered} q=\frac{-3-9}{2} \\ q=\frac{-12}{2} \\ q=-6 \end{gathered}$$

Conclusion

The solution of the quadratic equation is$q=3$and$q=-6$