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Completing the Square

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toni dimella
toni dimella

The document explains how to solve quadratic equations by completing the square. It defines a perfect square trinomial as having the form x^2 + bx + c, where c is the square of half of b. It provides steps for completing the square, which involves adding a constant term to both sides of the equation such that the left side becomes a perfect square trinomial that can be factorized. This process results in the solution(s) to the quadratic equation. Two examples demonstrating this process are included.

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Solving Quadratic Equations By Completing the Square
What is a Perfect Square Trinomial?
How to create a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. x 2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2) 2 X 2 + 14x + 49
Perfect Square Trinomials 100 4 25/4
How to Complete the Square Solve the following equation by completing the square: x 2 + 8x 20 = 0 Step 1: Move quadratic term, and linear term to left side of the equation x 2 + 8x = 20
Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. x 2 + 8x + ? = 20 + ? x 2 + 8x + 16 = 20 + 16 8/2 = 4 4 2 = 16
Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
Step 4: Take the square root of each side and solve. x = 10 or x = -2
Example #2 2 2 2
Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. x 2 7/2 + 49/16 = -6 + 49/16 x 2 7/2 + 49/16 = -96/16 + 49/16 x 2 7/2 + 49/16 = -47/16 遜 * 7/2 = 7/4 (7/4) 2 = 49/16
x 2 7/2 + 49/16 = -47/16 (x -7/2)(x -7/2) = -47/16 (x 7/2) 2 = -47/16 (x 7/2) 2 = -47/16 x -7/2 = i 47 Step 3: Factor the perfect square trinomial on the left side of the equation Step 4: Take the square root of each side 4 X = 7/2 + i 47 or x = 7/2 - i 47 4 4

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Completing the Square

  • 1. Solving Quadratic Equations By Completing the Square
  • 2. What is a Perfect Square Trinomial?
  • 3. How to create a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. x 2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2) 2 X 2 + 14x + 49
  • 5. How to Complete the Square Solve the following equation by completing the square: x 2 + 8x 20 = 0 Step 1: Move quadratic term, and linear term to left side of the equation x 2 + 8x = 20
  • 6. Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. x 2 + 8x + ? = 20 + ? x 2 + 8x + 16 = 20 + 16 8/2 = 4 4 2 = 16
  • 7. Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
  • 8. Step 4: Take the square root of each side and solve. x = 10 or x = -2
  • 10. Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. x 2 7/2 + 49/16 = -6 + 49/16 x 2 7/2 + 49/16 = -96/16 + 49/16 x 2 7/2 + 49/16 = -47/16 遜 * 7/2 = 7/4 (7/4) 2 = 49/16
  • 11. x 2 7/2 + 49/16 = -47/16 (x -7/2)(x -7/2) = -47/16 (x 7/2) 2 = -47/16 (x 7/2) 2 = -47/16 x -7/2 = i 47 Step 3: Factor the perfect square trinomial on the left side of the equation Step 4: Take the square root of each side 4 X = 7/2 + i 47 or x = 7/2 - i 47 4 4