Adapted from Walch Education Completing the Square Adapted from Walch Education

Perfect Square Trinomial can be written as the square of a binomial is called a perfect square trinomial When the binomial (x + a) is squared, the resulting perfect square trinomial is x2 + 2ax + a2. When the binomial (ax + b) is squared, the resulting perfect square trinomial is a2x2 + 2abx + b2. 5.2.3: Completing the Square

5.2.3: Completing the Square Completing the Square to Solve Quadratics Make sure the equation is in standard form, ax2 + bx + c. Subtract c from both sides. Divide each term by a to get a leading coefficient of 1. Add the square of half of the coefficient of the x-term to both sides to complete the square. Express the perfect square trinomial as the square of a binomial. Solve by using square roots. 5.2.3: Completing the Square

5.2.3: Completing the Square Practice Solve x2 + 6x + 4 = 0 by completing the square. 5.2.3: Completing the Square

5.2.3: Completing the Square Complete the Square x2 + 6x + 4 = 0 Original equation x2 + 6x = –4 Subtract 4 from both sides. x2 + 6x + 32 = –4 + 32 Add the square of half of the coefficient of the x-term to both sides to complete the square. x2 + 6x + 9 = 5 Simplify. 5.2.3: Completing the Square

Express the perfect square trinomial as the square of a binomial Half of b is 3, so the left side of the equation can be written as (x + 3)2. (x + 3)2 = 5 5.2.3: Completing the Square

5.2.3: Completing the Square Isolate x (x + 3)2 = 5 Equation Take the square root of both sides. Subtract 3 from both sides. The equation x2 + 6x + 4 = 0 has two solutions, 5.2.3: Completing the Square

5.2.3: Completing the Square Try this one. Solve 5x2 – 50x – 120 = 0 by completing the square. 5.2.3: Completing the Square

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