SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE PERFECT
SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE
PERFECT SQUARE TRINOMIALS l Examples l x 2 + 6 x + 9 l x 2 - 10 x + 25 l x 2 + 12 x + 36
l X 2 CREATING A PERFECT SQUARE TRINOMIAL + 14 x + ____ l Find the constant term by squaring half of b l (14/2)2 X 2 + 14 x + 49 l Factored this becomes (x+7)2 14/2 – half of b
PERFECT SQUARE TRINOMIALS l Create perfect square trinomials. l x 2 + 20 x + ___ l x 2 - 4 x + ___ l x 2 + 5 x + ___ 100 4 25/4
TO SOLVE BY COMPLETING THE SQUARE If a quadratic equation does not factor we can solve it by two different methods 1. ) Completing the Square (today’s lesson) 2. ) Quadratic Formula (tomorrow’s lesson)
STEPS TO SOLVE BY COMPLETING THE SQUARE 1. ) If the quadratic does not factor, move c to the other side of the equation, leave space on left! x²-4 x -7 =0 x²-4 x =7 2. ) Make the left side a perfect square trinomial and add number to both sides of equation x² -4 x 4/2= 2²=4 x² -4 x +4 = 7 +4 3. )Factor your trinomial square (x-2)² =11 4. )Solve by square roots method x-2 = ±√ 11 x = 2±√ 11
EXAMPLE Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation
SOLVING QUADRATIC EQUATIONS COMPLETING THE SQUARE Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. BY
Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE Step 4: Take the square root of each side
SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE Step 5: Set up the two possibilities and solve
SOLVING QUADRATIC EQUATIONS COMPLETING THE SQUARE BY Try the following examples. Do your work on your paper and then check your answers.
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