Finite Math Examples

$0.2 = \frac{x^{2}}{85 - x}$

Step 1

Subtract $\frac{x^{2}}{85 - x}$ from both sides of the equation.

$0.2 - \frac{x^{2}}{85 - x} = 0$

Step 2

Simplify $0.2 - \frac{x^{2}}{85 - x}$ .

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Step 2.1

To write $0.2$ as a fraction with a common denominator, multiply by $\frac{85 - x}{85 - x}$ .

$\frac{0.2 (85 - x)}{85 - x} - \frac{x^{2}}{85 - x} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{0.2 (85 - x) - x^{2}}{85 - x} = 0$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Factor $0.2$ out of $0.2 (85 - x) - x^{2}$ .

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Step 2.3.1.1

Reorder $85$ and $- x$ .

$\frac{0.2 (- x + 85) - x^{2}}{85 - x} = 0$

Step 2.3.1.2

Factor $0.2$ out of $- x^{2}$ .

$\frac{0.2 (- x + 85) + 0.2 (- 5 x^{2})}{85 - x} = 0$

Step 2.3.1.3

Factor $0.2$ out of $0.2 (- x + 85) + 0.2 (- 5 x^{2})$ .

$\frac{0.2 (- x + 85 - 5 x^{2})}{85 - x} = 0$

Step 2.3.2

Reorder terms.

$\frac{0.2 (- 5 x^{2} - x + 85)}{85 - x} = 0$

Step 2.4

Factor $- 1$ out of $- 5 x^{2}$ .

$\frac{0.2 (- (5 x^{2}) - x + 85)}{85 - x} = 0$

Step 2.5

Factor $- 1$ out of $- x$ .

$\frac{0.2 (- (5 x^{2}) - (x) + 85)}{85 - x} = 0$

Step 2.6

Factor $- 1$ out of $- (5 x^{2}) - (x)$ .

$\frac{0.2 (- (5 x^{2} + x) + 85)}{85 - x} = 0$

Step 2.7

Rewrite $85$ as $- 1 (- 85)$ .

$\frac{0.2 (- (5 x^{2} + x) - 1 (- 85))}{85 - x} = 0$

Step 2.8

Factor $- 1$ out of $- (5 x^{2} + x) - 1 (- 85)$ .

$\frac{0.2 (- (5 x^{2} + x - 85))}{85 - x} = 0$

Step 2.9

Rewrite $- (5 x^{2} + x - 85)$ as $- 1 (5 x^{2} + x - 85)$ .

$\frac{0.2 (- 1 (5 x^{2} + x - 85))}{85 - x} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{0.2 (5 x^{2} + x - 85)}{85 - x} = 0$

Step 3

Set the denominator in $\frac{0.2 (5 x^{2} + x - 85)}{85 - x}$ equal to $0$ to find where the expression is undefined.

$85 - x = 0$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $85$ from both sides of the equation.

$- x = - 85$

Step 4.2

Divide each term in $- x = - 85$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x = - 85$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 85}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 85}{- 1}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 85}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 85$ by $- 1$ .

$x = 85$

Step 5