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Completing the Square: A Guide to Quadratic Equations

Completing the square is a method used to solve quadratic equations and rewrite them in standard form. This guide outlines the essential steps: start by dividing everything by the leading coefficient if it's not 1, isolate the constant term, add a value to both sides without squaring, and rewrite the left side. It includes practical examples to find missing values and solve equations that aren't perfect squares, such as x² + 4x + 3 = 0 and 2x² = -16x + 18, illustrating how to complete the square effectively.

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Completing the Square: A Guide to Quadratic Equations

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Presentation Transcript

  1. Warm Up 5-7

  2. 5-7 Completing the Square ET: When looking at standard form of a quadratic equation, how can you determine if completing the square is a good option?

  3. Recall: • Steps to completing the square: • If a 1, divide everything by a • Isolate constant term • Add to both sides (do not square) • Rewrite left side as • Simplify right side • Take the square root of both sides (don’t forget on right) • Isolate x (will have 2 equations)

  4. Example 1Finding c to Complete the Square Find the missing value to complete the square.

  5. Example 2Solving When Not a Perfect Square Solve x2 + 4x + 3 = 0.

  6. Example 3Completing the Square when a 1 Solve 2x2 = -16x +18 .

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