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Wednesday 29th of June
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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Equations Quadratic in Form

In a quadratic equation we have a variable and its square (x and x2). An equation that contains an expression and the square of that expression is quadratic in form if substituting a single variable for that expression results in a quadratic equation. Equations that are quadratic in form can be solved by using methods for quadratic equations.

Example

An equation quadratic in form

Solve (x + 15)2 - 3(x + 15) - 18 = 0

Solution

Note that x + 15 and (x + 15)2 both appear in the equation. Let a = x + 15 and substitute a for x + 15 in the equation:

 (x + 15)2 - 3(x + 15) - 18 = 0 a2 - 3a - 18 = 0 (a - 6)(a + 3) = 0 Factor. a - 6 = 0 or a + 3 = 0 a = 6 or a = -3 x + 15 = 6 or x + 15 = -3 Replace a by x + 15. x = -9 or x = -18

Check in the original equation. The solution set is {-18, -9}.