How to Solve an Equation in GeoGebra

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

Solution in CAS

Open CAS under GeoGebra icon View in GeoGebra icon Menu.
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.
Click Solve GeoGebra icon in the Menubar to get the exact solution, or click Solve Numerically GeoGebra icon in the Menubar to solve numerically.

Screenshot of GeoGebra showing the solution of an equation

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

Solution in Graphics View

Choose Algebra View and Graphics View in the GeoGebra icon View menu.
Enter the expressions into two separate rows in the Algebra View and press Enter. Give the expressions fitting names.
Find the intersection between the graphs. You do this by typing

Intersect(<object>, <object>)

where the objects correspond to the two expressions. Press Enter.

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

f(x) = x2 2x 5 g(x) = 2x2 + x 15

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

Screenshot of GeoGebra showing the intersection of two graphs

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