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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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# Quadratic Equations with Imaginary Solutions

We can get imaginary solutions by completing the square.

Example 1

An equation with imaginary solutions

Find the complex solutions to x2 - 4x + 12 = 0.

Solution

Because the quadratic polynomial cannot be factored, we solve the equation by completing the square.

 x2 - 4x + 12 = 0 The original equation x2 - 4x = -12 Subtract 12 from each side. x2 - 4x + 4 = -12 + 4 One-half of -4 is -2, and (-2)2 = 4. (x - 2)2 = -8 x - 2 = Â± Even-root property x = 2 Â± i x =

Check these values in the original equation. The solution set is {}.