Q. 29 - Precalculus Enhanced with Graphing Utilities

Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$3x^2=4x+4$

Step-by-Step Solution

Answer

The required solution is $x=-\frac{2}{3},2$ and the graph of the solution is shown below:

Step 1. Given information.

We have:

$3x^2=4x+4$

Step 2. Solve the equation algebraically.

The equation is $3x^2=4x+4$.

$3x^2-4x-4=0$

For a quadratic equation of the form $a{x}^2+bx+c=0$ the solutions are:

$x_{1,\hspace{0.17em}2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For $a=3,\hspace{0.17em}b=-4,\hspace{0.17em}c=-4$

$$\begin{gathered} x_{1,\hspace{0.17em}2}=\frac{-\left(-4\right)\pm \sqrt{{\left(-4\right)}^2-4·\hspace{0.17em}3\left(-4\right)}}{2·\hspace{0.17em}3} \\ {x}_{1,\hspace{0.17em}2}=\frac{-\left(-4\right)\pm \hspace{0.17em}8}{2·\hspace{0.17em}3} \\ x=2,\hspace{0.17em}-\frac{2}{3} \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x=2,-\frac{2}{3}$.

Draw the graph of the equation $3x^2=4x+4$ using the graphing utility: