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Mastering the Technique of Completing the Square in Quadratic Equations

This guide explores the method of completing the square for quadratic trinomials, with specific emphasis on perfect square trinomials. Learn how to factor expressions like x² + 6x + 9 into (x + 3)² and understand the step-by-step process for any quadratic expression of the form x² + bx. The guide includes essential steps to rewrite and manipulate equations efficiently, ensuring clarity in solving quadratic equations. Ideal for students and educators seeking to deepen their understanding of this fundamental algebraic technique.

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Mastering the Technique of Completing the Square in Quadratic Equations

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  1. Factor Using “COMPLETING THE SQUARE” Look at these trinomials that are perfect square trinomials. x2 + 6x + 9 = ( x + 3 ) 2x2 – 12x + 36 = ( x – 6 ) 2 Notice: Factoring using “Perfect Square Trinomials” or the “T” Method will give you the square of the binomial outcome. To complete the square for an expression in the form x2 + bx, you must add to the expression. Examples: Find n to complete the square. 1. 2. 3. STEPS TO COMPLETE THE SQUARE: 1) 2) 3) 4) 5) 6) The constant is always the square of half of the coefficient of the x-term. Or If the leading coefficient is NOT one, divide both sides by the leading coefficient TO MAKE IT A ONE. Rewrite the equation in the form x2 + bx = c Complete the square by adding to both sides Write the trinomial as a square Solve the equation using legal algebra moves Round to the nearest hundredth

  2. Examples: 4. 6. 5. 7.

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