Quadratic Equations with Imaginary Solutions

Example

Solve using the quadratic formula: 2x² + 7 = 3x.

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Solution

Step 1	Write the quadratic equation in standard form. Subtract 3x from both sides of the equation.	2x2 - 3x + 7 = 0
Step 2	Identify the values of a, b, and c. a = 2, b = -3, c = 7
Step 3	Substitute the values of a, b, and c into the quadratic formula.
	Substitute 2 for a, -3 for b, and 7 for c.
Step 4	Simplify. Simplify the radicand and the denominator.
	Use to simplify the square root.
	Write the final answer in the form a + bi.
Step 5	Check each solution. We leave the check to you.

Notice that the solutions are complex conjugates.