Algebra Examples

$| \sqrt{x} - 4 | = 2$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$\sqrt{x} - 4 = \pm 2$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$\sqrt{x} - 4 = 2$

Step 2.2

Move all terms not containing $\sqrt{x}$ to the right side of the equation.

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Step 2.2.1

Add $4$ to both sides of the equation.

$\sqrt{x} = 2 + 4$

Step 2.2.2

Add $2$ and $4$ .

$\sqrt{x} = 6$

Step 2.3

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x}}^{2} = 6^{2}$

Step 2.4

Simplify each side of the equation.

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Step 2.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = 6^{2}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

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Step 2.4.2.1.1

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 2.4.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 2.4.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.4.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 2.4.2.1.1.2.2

Rewrite the expression.

$x^{1} = 6^{2}$

Step 2.4.2.1.2

Simplify.

$x = 6^{2}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Raise $6$ to the power of $2$ .

$x = 36$

Step 2.5

Next, use the negative value of the $\pm$ to find the second solution.

$\sqrt{x} - 4 = - 2$

Step 2.6

Move all terms not containing $\sqrt{x}$ to the right side of the equation.

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Step 2.6.1

Add $4$ to both sides of the equation.

$\sqrt{x} = - 2 + 4$

Step 2.6.2

Add $- 2$ and $4$ .

$\sqrt{x} = 2$

Step 2.7

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x}}^{2} = 2^{2}$

Step 2.8

Simplify each side of the equation.

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Step 2.8.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = 2^{2}$

Step 2.8.2

Simplify the left side.

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Step 2.8.2.1

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

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Step 2.8.2.1.1

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 2.8.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 2.8.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.8.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 2.8.2.1.1.2.2

Rewrite the expression.

$x^{1} = 2^{2}$

Step 2.8.2.1.2

Simplify.

$x = 2^{2}$

Step 2.8.3

Simplify the right side.

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Step 2.8.3.1

Raise $2$ to the power of $2$ .

$x = 4$

Step 2.9

The complete solution is the result of both the positive and negative portions of the solution.

$x = 36, 4$