Question

In the following exercises, solve by using the Quadratic Formula.
$16c^2+24c+9=0$

Short answer

The solution of the given equation is $c=-\frac{3}{4}$.

Step-by-step solution

Step 1. Given information

The given equation is:

$16c^2+24c+9=0$

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a{x}^2+bx+c=0$is:

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

In the given equation, $a=16,b=24,c=9$. Substitute these values in Quadratic Formula.

$c=\frac{-24\pm \sqrt{(24{)}^2-4(16\left)\right(9)}}{2\left(16\right)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl}c& =& \frac{-24\pm \sqrt{576-576}}{32}\\ c& =& \frac{-24\pm 0}{32}\\ c& =& \frac{-24}{32}\\ c& =& -\frac{3}{4}\end{array}$

Step 4. Conclusion.

The solution of the given equation is $c=-\frac{3}{4}$.