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Chapter Contents

• Quadratic Equations
• 1. Solving Quadratic Equations by Factoring
• 2. Completing the Square
• 3. The Quadratic Formula
• 4. The Graph of the Quadratic Function
• 5. Equations in Quadratic Form

• Comments, Questions?

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3. The Quadratic Formula

Using the method of completing the square, we can derive a general formula for solving quadratic equations:

For any quadratic equation ax² + bx + c = 0, the solutions for x can be found by using the quadratic formula:

Example 1:

Solve 2x² - 7x - 5 = 0

 

Answer

By inspection, we can see that: a = 2, b = -7 and c = -5

Substituting these into the quadratic formula, we get :

Here is a LiveMath document to illustrate this formula.

LIVEMath

Example 2:

Solve 2x² = 4x + 3

Answer

Exercise

Solve 6r² = 6r + 1 using the quadratic formula.

Answer