Basic Math Examples

$0.006 q = \frac{3000}{q} + 0.003 q$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, q, 1$

Step 1.2

The LCM of one and any expression is the expression.

$q$

Step 2

Multiply each term in $0.006 q = \frac{3000}{q} + 0.003 q$ by $q$ to eliminate the fractions.

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Step 2.1

Multiply each term in $0.006 q = \frac{3000}{q} + 0.003 q$ by $q$ .

$0.006 q \cdot q = \frac{3000}{q} q + 0.003 q \cdot q$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $q$ by $q$ by adding the exponents.

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Step 2.2.1.1

Move $q$ .

$0.006 (q \cdot q) = \frac{3000}{q} q + 0.003 q \cdot q$

Step 2.2.1.2

Multiply $q$ by $q$ .

$0.006 q^{2} = \frac{3000}{q} q + 0.003 q \cdot q$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $q$ .

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Step 2.3.1.1.1

Cancel the common factor.

$0.006 q^{2} = \frac{3000}{q} q + 0.003 q \cdot q$

Step 2.3.1.1.2

Rewrite the expression.

$0.006 q^{2} = 3000 + 0.003 q \cdot q$

Step 2.3.1.2

Multiply $q$ by $q$ by adding the exponents.

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Step 2.3.1.2.1

Move $q$ .

$0.006 q^{2} = 3000 + 0.003 (q \cdot q)$

Step 2.3.1.2.2

Multiply $q$ by $q$ .

$0.006 q^{2} = 3000 + 0.003 q^{2}$

Step 3

Solve the equation.

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Step 3.1

Move all terms containing $q$ to the left side of the equation.

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Step 3.1.1

Subtract $0.003 q^{2}$ from both sides of the equation.

$0.006 q^{2} - 0.003 q^{2} = 3000$

Step 3.1.2

Subtract $0.003 q^{2}$ from $0.006 q^{2}$ .

$0.003 q^{2} = 3000$

Step 3.2

Divide each term in $0.003 q^{2} = 3000$ by $0.003$ and simplify.

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Step 3.2.1

Divide each term in $0.003 q^{2} = 3000$ by $0.003$ .

$\frac{0.003 q^{2}}{0.003} = \frac{3000}{0.003}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $0.003$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{0.003 q^{2}}{0.003} = \frac{3000}{0.003}$

Step 3.2.2.1.2

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

$q^{2} = \frac{3000}{0.003}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $3000$ by $0.003$ .

$q^{2} = 1000000$

Step 3.3

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

$q = \pm \sqrt{1000000}$

Step 3.4

Simplify $\pm \sqrt{1000000}$ .

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Step 3.4.1

Rewrite $1000000$ as $1000^{2}$ .

$q = \pm \sqrt{1000^{2}}$

Step 3.4.2

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

$q = \pm 1000$

Step 3.5

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

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Step 3.5.1

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

$q = 1000$

Step 3.5.2

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

$q = - 1000$

Step 3.5.3

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

$q = 1000, - 1000$