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Warm Up 4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.

Warm Up 4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3. 4. ( x + 7)( x – 4) = 0 5. x 2 – 11 x + 30 = 0 6. x 2 = 2 x + 15. 4. – 2. 35. – 7, 4. 6, 5. 5, – 3. Objective. Solve radical equations. Vocabulary. radical equation extraneous solution.

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Warm Up 4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.

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  1. Warm Up 4-22-09 • Solve each equation. • 1. 3x +5 = 17 • 2. 4x + 1 = 2x – 3 • 3. • 4. (x + 7)(x – 4) = 0 • 5. x2 – 11x + 30 = 0 • 6.x2 = 2x + 15 4 –2 35 –7, 4 6, 5 5, –3

  2. Objective Solve radical equations.

  3. Vocabulary radical equation extraneous solution

  4. A radical equation is an equation that contains a variable within a radical. In this course, you will only study radical equations that contain square roots. Recall that you use inverse operations to solve equations. For nonnegative numbers, squaring and taking the square root are inverse operations. When an equation contains a variable within a square root, square both sides of the equation to solve.

  5. Directions: Solve the equation. Check your answer.

  6. Check 5 5 5 Example 1 x = 25 

  7. Check 10 10 Example 2 100 = 2x 50 = x 

  8. Check  Example 3 3x = 1

  9. Some square-root equations do not have the square root isolated. To solve these equations, you may have to isolate the square root beforesquaring both sides. You can do this by using one or more inverse operations.

  10. Check Example 4 x = 81 9 – 4 5  5 5

  11. Check  7 7 Example 5 x = 46

  12. Example 6 5x + 1 = 16 5x = 15 x = 3

  13. Check Example 6 Continued 4 + 6 10  10 10

  14. Example 7 Method 1 x = 64

  15. Example 7 Continued Method 2 x = 64

  16. Check Example 7 Continued  32 32

  17. Example 8 Method 1 144 = x

  18. Example 8 Continued Method 2 144 = x

  19. Example 8 Continued Check  12 12

  20. Example 9 Method 1 x = 100

  21. Example 9 Continued Method 2 4x = 400 x = 100

  22. Check 4 Example 9 Continued 4 4 

  23. Lesson Summary Solve each equation. Check your answer. 1. 2. 36 45 no solution 3. 4. 11

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