Algebra Examples

$x - 12 x \sqrt{x} = 0$

Step 1

Factor $x$ out of $x - 12 x \sqrt{x}$ .

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Step 1.1

Raise $x$ to the power of $1$ .

$x - 12 x \sqrt{x} = 0$

Step 1.2

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - 12 x \sqrt{x} = 0$

Step 1.3

Factor $x$ out of $- 12 x \sqrt{x}$ .

$x \cdot 1 + x (- 12 \sqrt{x}) = 0$

Step 1.4

Factor $x$ out of $x \cdot 1 + x (- 12 \sqrt{x})$ .

$x (1 - 12 \sqrt{x}) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$1 - 12 \sqrt{x} = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $1 - 12 \sqrt{x}$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $1 - 12 \sqrt{x}$ equal to $0$ .

$1 - 12 \sqrt{x} = 0$

Step 4.2

Solve $1 - 12 \sqrt{x} = 0$ for $x$ .

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Step 4.2.1

Subtract $1$ from both sides of the equation.

$- 12 \sqrt{x} = - 1$

Step 4.2.2

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

${(- 12 \sqrt{x})}^{2} = {(- 1)}^{2}$

Step 4.2.3

Simplify each side of the equation.

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Step 4.2.3.1

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

${(- 12 x^{\frac{1}{2}})}^{2} = {(- 1)}^{2}$

Step 4.2.3.2

Simplify the left side.

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Step 4.2.3.2.1

Simplify ${(- 12 x^{\frac{1}{2}})}^{2}$ .

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Step 4.2.3.2.1.1

Apply the product rule to $- 12 x^{\frac{1}{2}}$ .

${(- 12)}^{2} {(x^{\frac{1}{2}})}^{2} = {(- 1)}^{2}$

Step 4.2.3.2.1.2

Raise $- 12$ to the power of $2$ .

$144 {(x^{\frac{1}{2}})}^{2} = {(- 1)}^{2}$

Step 4.2.3.2.1.3

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

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Step 4.2.3.2.1.3.1

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

$144 x^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Step 4.2.3.2.1.3.2

Cancel the common factor of $2$ .

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Step 4.2.3.2.1.3.2.1

Cancel the common factor.

$144 x^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Step 4.2.3.2.1.3.2.2

Rewrite the expression.

$144 x^{1} = {(- 1)}^{2}$

Step 4.2.3.2.1.4

Simplify.

$144 x = {(- 1)}^{2}$

Step 4.2.3.3

Simplify the right side.

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Step 4.2.3.3.1

Raise $- 1$ to the power of $2$ .

$144 x = 1$

Step 4.2.4

Divide each term in $144 x = 1$ by $144$ and simplify.

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Step 4.2.4.1

Divide each term in $144 x = 1$ by $144$ .

$\frac{144 x}{144} = \frac{1}{144}$

Step 4.2.4.2

Simplify the left side.

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Step 4.2.4.2.1

Cancel the common factor of $144$ .

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Step 4.2.4.2.1.1

Cancel the common factor.

$\frac{144 x}{144} = \frac{1}{144}$

Step 4.2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{144}$

Step 5

The final solution is all the values that make $x (1 - 12 \sqrt{x}) = 0$ true.

$x = 0, \frac{1}{144}$