Question

Solve each equation by using the method of your choice. Find exact solutions.

Answer 1

Given the quadratic equation:

$16x^2-24x-27=0$

To find the solutions for the given equation you have to apply the quadratic formula:

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

Where

a is the coefficient of the quadratic term

b is the coefficient of the x-term

c is the constant of the equation

For this equation, a= 16, b= -24, and c= -27, replace the values into the formula:

$\begin{gathered} x=\frac{-(-24)\pm\sqrt[]{(-24)^2-4\cdot16\cdot(-27)}}{2\cdot16} \\ x=\frac{24\pm\sqrt[]{576+1728}}{32} \\ x=\frac{24\pm\sqrt[]{2304}}{32} \\ x=\frac{24\pm48}{32} \end{gathered}$

Solve the addition and subtraction separately to determine both possible values of x:

-Addition:

$\begin{gathered} x=\frac{24+48}{32} \\ x=\frac{72}{32} \\ x=\frac{9}{4} \end{gathered}$

-Subtraction

$\begin{gathered} x=\frac{24-48}{32} \\ x=-\frac{24}{32} \\ x=-\frac{3}{4} \end{gathered}$

The solutions of the quadratic equation are x=9/4 and x=-3/4