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Friday 23rd of March
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

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 Solve for:

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# Solving Quadratic Equations by Completing the Square

There are some equations where the solutions are rational numbers, and the equation can be solved by factoring.

In the next example the solutions are irrational numbers, and factoring will not work.

Example 1

A quadratic equation with irrational solutions

Solve x2 - 3x - 6 = 0 by completing the square.

Solution

Because a = 1, we first get the x2 and x terms on the left-hand side:

 x2 - 3x - 6 = 0 x2 - 3x = 6 Add 6 to each side. Even-root property x Add to each side. x

The solution set is .