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A quadratic equation is one in which the highest power is 2. For example, x² + 5x + 6 = 0

Method When Equation is Equal to Zero

The right hand side must be 0 in order to use the following method.

Example 1: Solve x² + 5x + 6 = 0

Step 1: Factorise the quadratic

Step 2: Put each factor equal to 0

(Note: if two brackets are multiplied to give 0, then one of them must be 0).

Step 3: Solve these two simple equations.

Therefore –3 and –2 are the solutions of the equation.

There are two solutions because of the shape of the graph (refer to study note on graphs).

Example 2: Solve x² + 7x – 18 = 0

Example 3: Solve x² – 8x + 12 = 0

Method When Equation is Not Equal to Zero

If the equation given is not equal to zero, then follow this procedure.

Example 1: Solve x ² + 5x + 3 = 17

Make the right side equal to zero by subtracting 17 from both sides.