Exercise Solve x – 14 = 35. x = 49.

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Presentation transcript:

Exercise Solve x – 14 = 35. x = 49

Exercise Solve 6x = 108. x = 18

Exercise Solve 9x + 14 = – 49. x = – 7

Exercise Solve 4x – 81 = 99. x = 45

Exercise Solve 6(3x – 13) = 84. x = 9

Radical Equation A radical equation is an equation that contains a variable in a radicand. Example: √ x = 5

Remember: 62 = 36, so √ 36 = 6. In general, (√ x )2 = x and (√ x + 3 )2 = x + 3.

When solving, be sure to square both sides of the radical equation.

Example 1 Solve √ x = 5. √ x = 5 √ x = 5 (√ x )2 = 52 √ 25 = 5 x = 25

There is no number that makes this equation true. Example 2 Solve and check √ x = – 8. √ x = – 8 √ x = – 8 (√ x )2 = (– 8)2 √ 64 = – 8 x = 64 8 = – 8; false There is no number that makes this equation true.

Solving Radical Equations Isolate the radical on one side of the equation. 2. Square both sides of the equation. 3. Solve the resulting equation, if necessary. 4. Check the solution.

Example 3 Solve and check √ 3x + 2 = 8. √ 3x + 2 = 8

Example 3 Solve and check √ 3x + 2 = 8. x = 12 √ 3(12) + 2 = 8 √ 36 + 2 = 8 6 + 2 = 8 8 = 8

Example 4 Solve and check √ 10 + x + 6 = 7. √ 10 + x + 6 = 7

Example 4 Solve and check √ 10 + x + 6 = 7. 10 + x = 1 √ 10 + (– 9) + 6 = 7 1 + 6 = 7 √ 1 + 6 = 7 7 = 7

The equation has no real solution. Example 5 Solve – 4 √ x = 28. – 4 √ x = 28 – 4 √ x = – 7 The equation has no real solution.

Example Solve √ x = 6. x = 36

Example Solve √ x + 3 = 8. x = 61

Example Solve √ x + 3 = 8. x = 25

Example Solve 2 √ x = 8. x = 16

Example Solve √ 2x = 8. x = 32

Example Solve √ 3x – 1 = 2. x = 5 3

Example Solve √ 1 – x = 4. x = – 15

Example Solve 4 √ 2x – 5 + 6 = 22. x = 21 2

Example Solve √ 2x + 1 = √ x + 5. x = 4

Exercise The square root of a number, decreased by 2, is 4. Find the number. n = 36

Exercise The square root of the result of decreasing a number by 2 is 4. Find the number. n = 18

Exercise Seven more than the square root of a number is 12. Find the number. n = 25

Exercise The square root of 7 more than a number is 12. Find the number. n = 137