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7.5 More Quadratic Equations BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Solution: This equation has fractions in it. How do we clear the fractions? Multiply all of the terms by the LCD, n(n + 4). Then we solve using an appropriate method. Also, we must note which values of n will cause division by 0, and exclude those from our solution. 0 = (n + 12)(n – 2) Answer: {– 12, 2} So far, we have worked with 3 different methods for solving quadratic equations. We have solved by: factoring, completing the square, and using the quadratic formula. In this section we will look at two types of equations and their methods of solutions. Example 1. Your Turn Problem #1

7.5 More Quadratic Equations BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 Solution:Although this is not a quadratic (2 nd degree) equation, it is in quadratic form. You may recall this equation is still factorable if we can find two numbers whose product is the last number and whose difference is the middle number. Since we have x 4, we will have x 2 in both first positions of the parentheses. Also, this can still be factored by grouping if you wish. Example 2. Solve: x 4 + 5x 2 – 84 = 0 or by grouping, Your Turn Problem #2

7.5 More Quadratic Equations BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 Applications “Applications” means word problems. Here’s a reminder of steps to take when solving word problems. 1.Choose a meaningful variable to represent the unknown quantity. Represent any other unknowns in terms of that variable. 2.Sketch any figure, chart, or diagram that might be helpful in analyzing the problem if possible. 3. Look for a guideline that you can use to set up an equation. Is there a formula we can use? Are we translating? Etc. 4. Set up the equation. 5. Solve the equation. Next Slide 6. Answer the question.