Q. 27 - Precalculus Enhanced with Graphing Utilities

Question

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

$x^2-3x-28=0$

Step-by-Step Solution

Answer

The required solution is $x=-4,7$ and the graph is shown below:

Step 1. Given information.

We have:

$x^2-3x-28=0$

Step 2. Solve the equation algebraically.

The equation is $x^2-3x-28=0$.

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 $a=1,\hspace{0.17em}b=-3,\hspace{0.17em}c=-28$

$$\begin{gathered} x_{1,\hspace{0.17em}2}=\frac{-\left(-3\right)\pm \sqrt{{\left(-3\right)}^2-4·\hspace{0.17em}1·\left(-28\right)}}{2·\hspace{0.17em}1} \\ {x}_{1,\hspace{0.17em}2}=\frac{-\left(-3\right)\pm \hspace{0.17em}11}{2·\hspace{0.17em}1} \\ x=-4,7 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x=-4,7.$

Draw the graph of the equation $x^2-3x-28=0$ using the graphing utility: