Question

Solve by using the quadratic formula.

$2w^2+9w+2=0$

Short answer

The solution is$w=\frac{-9\pm \sqrt{65}}{4}$.

Step-by-step solution

Step 1. Given information.

The given equation is$2w^2+9w+2=0$.

Step 2. Write the equation in standard form.

The standard quadratic equation is $a{w}^2+bw+c=0$.

$2w^2+9w+2=0$

So, here$a=2,b=9,c=2$.

Step 3. Apply the quadratic formula.

The quadratic formula is $w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

Substitute $a=2,b=9,c=2$in the above formula.

$\begin{array}{rcl}w& =& \frac{-9\pm \sqrt{9^2-4\times 2\times 2}}{2\left(2\right)}\\ & =& \frac{-9\pm \sqrt{81-16}}{4}\\ & =& \frac{-9\pm \sqrt{65}}{4}\end{array}$

Step 4. Simplified answer.

Hence, the required solution is$w=\begin{array}{rcl}& & \frac{-9\pm \sqrt{65}}{4}\end{array}$.