How to Get Rid of a Variable That Is Cubed

How to Get Rid of a Variable That Is Cubed
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An exponent represents how many times a number should be multiplied by itself. For example, ​x3 (or x cubed) would be written out as ​x​ × ​x​ × ​x​. Canceling out a component in an equation requires using the opposite of that component. For example, subtracting 4 eliminates positive 4. The opposite of exponents are roots. The opposite of an exponent of 3 is a cubed root, indicated by this symbol: ³√.

    Isolate the instances of the cubed variable on one side of the equation. Practice using the example

    2x^3 + 2 = 3 - 6x^3

    First, add 6​x3 to both sides. This leaves you with:

    8x^3 + 2 = 3

    Next, subtract 2 from both sides to isolate the variable:

    8x^3 = 1

    Eliminate the leading number or coefficient of the variable as the exponent only applies to the variable, not to that number. To continue the example, divide both sides of 8​x3 = 1 by 8 to obtain

    x^3 = \frac{1}{8}

    Eliminate the cube on the variable by taking the cube root of both sides of the equation:

    \sqrt[3]{x^3}= \sqrt[3]{\frac{1}{8}} \text{ or } x = \sqrt[3]{\frac{1}{8}}

    Simplify the answer. Because the cube root of 8 is 2:

    \sqrt[3]{\frac{1}{8}} = \frac{1}{2} \text{ So }x = \frac{1}{2}

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