Pre-Algebra Examples

$3 {(0.1 x)}^{2} \cdot 0.1 = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Factor.

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Step 1.1.1

Apply the product rule to $0.1 x$ .

$3 ({0.1}^{2} x^{2}) \cdot 0.1 = 0$

Step 1.1.2

Remove unnecessary parentheses.

$3 \cdot ({0.1}^{2} x^{2}) \cdot 0.1 = 0$

Step 1.2

Combine exponents.

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Step 1.2.1

Multiply $0.1$ by $3$ .

$0.3 \cdot ({0.1}^{2} x^{2}) = 0$

Step 1.2.2

Multiply $0.3$ by ${0.1}^{2}$ .

$0.003 x^{2} = 0$

Step 2

Divide each term in $0.003 x^{2} = 0$ by $0.003$ and simplify.

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Step 2.1

Divide each term in $0.003 x^{2} = 0$ by $0.003$ .

$\frac{0.003 x^{2}}{0.003} = \frac{0}{0.003}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.003$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.003 x^{2}}{0.003} = \frac{0}{0.003}$

Step 2.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{0.003}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $0.003$ .

$x^{2} = 0$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Step 4

Simplify $\pm \sqrt{0}$ .

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Step 4.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 4.3

Plus or minus $0$ is $0$ .

$x = 0$