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Sunday 15th of September
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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:

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 Ineq. #9:

 Solve for:

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Miscellaneous Equations

The following examples shows an equation that is not originally in the form of a quadratic equation. However, after simplifying this equation, we get a quadratic equation. Even though completing the square can be used on any quadratic equation, factoring and the square root property are usually easier and we can use them when applicable. In the next example we will use the most appropriate method.

Example

Solve

Solution

Square both sides of the equation to eliminate the radical:

 x + 3 The original equation (x + 3)2 Square each side. x2 + 6x + 9 153 - x Simplify. x2 + 7x - 144 = 0 (x - 9)(x + 16) = 0 Factor. x - 9 = 0 or x + 16 = 0 Zero factor property x = 9 or x = -16

Because we squared each side of the original equation, we must check for extraneous roots. Let x = 9 in the original equation:

Let x = -16 in the original equation:

Because -16 is an extraneous root, the solution set is {9}.