what are the steps used to solve an equation with radical ex

what are the steps used to solve an equation with radical expressions?

Solution

To solve a radical equation, follow these steps:

1) Get a radical alone on one side of the equation. It\'s OK if there is a constant times the radical.

2) Raise both SIDES of the equation to a power equal to the index number of the radical that is alone. When that lone radical is raised to that power, the radical and the power cancel each other out. If there was a number out front, that number is raised to that power and is multiplied times the expression that used to be inside the radical.

3) Combine any like terms from both sides. If there is still another radical, get it alone and repeat step 2. If all radicals are gone, solve the equation.

4) Raising thing to powers can sometimes introduce extraneous roots. These are numbers that might check into your equation after the radicals are eliminated, but they do not check in the original problem. To see if an answer is good or is extraneous, it must be checked in the original equation. Since extraneous solutions do not check in the original equation, they are not correct and should be discarded.
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2x + 4 = x
Get the radical alone.

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2x = x - 4
Square both sides.

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(2x)² = (x - 4)²

2x = (x - 4)²
2x = x² - 8x + 16
x² - 10x + 16 = 0
(x - 8)(x - 2) = 0
x =8 or x = 2

Now check each answer by substituting them into the original problem.

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2x + 4 = x
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2(8) + 4 = 8
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16 + 4 = 8
4 + 4 = 8
8 = 8 This answer checks, so x = 8 is a good answer.

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2x + 4 = x
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2(2) + 4 = 2
.._
4 + 4 = 2
2 + 4 = 2
6 2 The answer x = 2 did not check, so discard it.

The answer is only x = 8. x = 2 was an extraneous root. <==ANSWER