1. Solving Radical Equations

2. that contains a radical.
A radical equation
is an equation
that contains a radical.
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3. in solving most equations.
The goal in solving
radical equations
is the same as the goal
in solving most equations.
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4. We need to isolate
the variable.
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5. But there is only one way
to move the variable
out from under the
square root sign.
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6. We need to square the
radical expression.
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7. And, because it is an
equation,
what we do to one side,
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8. we have to do to the other.
And, because it is an
equation,
what we do to one side,
we have to do to the other.
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9. (Even if n is an expression)
Remember,
no matter what
n is.
(Even if n is an expression)
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10. So we have:
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12. Solve for x:
Step 1. Simplify the expression:
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13. Solve for x:
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14. Solve for x: Step 1. Simplify the expression.
Step 2. Isolate the radical.
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15. Solve for x:
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16. Solve for x: Step 1. Simplify the expression.
Step 2. Isolate the radical.
Step 3. Square both sides.
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17. Solve for x:
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18. Solve for x: Step 1. Simplify the expression.
Step 2. Isolate the radical.
Step 3. Square both sides.
Step 4. Solve the equation.
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19. Solve for x:
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20. Try this one:
Dude! You try one.
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21. BACK

22. BACK

23. Try this one:
Dude! You try one.
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25. No Solutions
If you have a square root equaling a negative number there is no solution.

26. An Extraneous Solution is a solution that does not satisfy the original equation.
-2 is an extraneous answer.

27. Watch Out!!
If all answers are extraneous, there is also no solution.

29. Since -11 does not satisfy the original equation, 11 is the only solution is an extraneous solution.

30. Solving Radical Equations
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