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=(24\pm48)/(32) \end{gathered}`

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

-Addition:

`\begin{gathered} x=(24+48)/(32) \\ x=(72)/(32) \\ x=(9)/(4) \end{gathered}`

-Subtraction

`\begin{gathered} x=(24-48)/(32) \\ x=-(24)/(32) \\ x=-(3)/(4) \end{gathered}`

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