You can solve equations either symbolically or numerically. `GeoGebra`

solves them automatically when you enter them in `CAS`

and click `Symbolic Evaluation`

or `Numeric Evaluation`

. `Symbolic Evaluation`

gives you the exact solution, while `Numeric Evaluation`

gives you the solution as a possibly approximated decimal number.

If you get $\{\}$ as the output, then the equation has no solution. If you get $\{x=a\}$, the equation has one solution, and if you get $\{x=a,x=b\}$, the equation has two solutions. **Note!** Here $a$ and $b$ represent numbers.

`GeoGebra`

Instruction 1

`CAS`

- 1.
- Open
`CAS`

under`View`

in`Menu`

. - 2.
- Enter the equation in the
`CAS`

window. If the right-hand side of the equation is 0, you only need to type the expression on the left-hand side. - 3.
- Click
`Solve`

in the`Menubar`

to get the exact solution, or click`Solve Numerically`

in the`Menubar`

to solve numerically.

Solving an equation graphically is the same as drawing the graph of the expressions on each side of the equation, and finding the $x$-coordinate of the intersection between the graphs.

`GeoGebra`

Instruction 2

`Graphics View`

- 1.
- Choose
`Algebra View`

and`Graphics View`

in the`View`

menu. - 2.
- Enter the expressions into two separate rows in the
`Algebra View`

and press`Enter`

. Give the expressions fitting names. - 3.
- Find the intersection between the graphs. You do this by typing
Intersect(<object>, <object>)

where the objects correspond to the two expressions. Press

`Enter`

. - 4.
- If the equation has any solutions, you can find them in the
`Algebra View`

.

Example 1

**Solve the equation **

$$f(x)=g(x)$$ |

graphically, where $$\begin{array}{llll}\hfill f(x)& ={x}^{2}-2x-5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill g(x)& =2{x}^{2}+x-15\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

The picture below shows the solutions to the equation that you get by following the instructions above.

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