1. 4-6 COMPLETING THE SQUARE Ms. Miller

2. TODAY’S OBJECTIVE To learn to solve quadratic equations by Finding square roots Completing the square

3. SOLVING BY FINDING SQUARE ROOTS You can solve an equation that contains a perfect square by finding the square roots. Simplest form of this: 1. 2.

4. SOLVING A PERFECT SQUARE TRINOMIAL EQUATION Sometimes, an equation will have a perfect square trinomial equal to a constant. We can solve by factoring, then find the square roots. Perfect square trinomial constant or

5. COMPLETING THE SQUARE If is not part of a perfect square trinomial, you can use b to find a constant c so that is a perfect square. To make a perfect square trinomial, add What value completes the square for ? Step 1: Identify b Step 2: Calculate Step 3: Rewrite the expression

6. Step 1: Rewrite in the form Divide all terms by the coefficient of if it is not 1 SOLVING AN EQUATION BY COMPLETING THE SQUARE What is the solution of ? Step 2: Complete the square & add to both sides of the equation Step 3: Rewrite the expression & factor Step 3: Find the square roots & solve for x or

7. TRY THESE What are the solutions? Solve by completing the square. 1.2. or

8. DETERMINING DIMENSIONS The lengths of the sides of a rectangular window have the ratio 1.6 to 1. The area of the window is 2822.4 in2. What are the window dimensions? 1.6x x The window dimensions are 42 inches x 67.2 inches