Finite Math Examples

$(30 x) = 0.1 x^{2} + 7 x + 400$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Remove parentheses.

$30 x = 0.1 x^{2} + 7 x + 400$

Step 1.2

Move all the expressions to the left side of the equation.

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Step 1.2.1

Subtract $0.1 x^{2}$ from both sides of the equation.

$30 x - 0.1 x^{2} = 7 x + 400$

Step 1.2.2

Subtract $7 x$ from both sides of the equation.

$30 x - 0.1 x^{2} - 7 x = 400$

Step 1.2.3

Subtract $400$ from both sides of the equation.

$30 x - 0.1 x^{2} - 7 x - 400 = 0$

Step 1.3

Subtract $7 x$ from $30 x$ .

$- 0.1 x^{2} + 23 x - 400 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = - 0.1$ , $b = 23$ , and $c = - 400$ into the quadratic formula and solve for $x$ .

$\frac{- 23 \pm \sqrt{23^{2} - 4 \cdot (- 0.1 \cdot - 400)}}{2 \cdot - 0.1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $23$ to the power of $2$ .

$x = \frac{- 23 \pm \sqrt{529 - 4 \cdot - 0.1 \cdot - 400}}{2 \cdot - 0.1}$

Step 4.1.2

Multiply $- 4 \cdot - 0.1 \cdot - 400$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 0.1$ .

$x = \frac{- 23 \pm \sqrt{529 + 0.4 \cdot - 400}}{2 \cdot - 0.1}$

Step 4.1.2.2

Multiply $0.4$ by $- 400$ .

$x = \frac{- 23 \pm \sqrt{529 - 160}}{2 \cdot - 0.1}$

Step 4.1.3

Subtract $160$ from $529$ .

$x = \frac{- 23 \pm \sqrt{369}}{2 \cdot - 0.1}$

Step 4.2

Multiply $2$ by $- 0.1$ .

$x = \frac{- 23 \pm \sqrt{369}}{- 0.2}$

Step 4.3

Simplify $\frac{- 23 \pm \sqrt{369}}{- 0.2}$ .

$x = 115 \pm 96.04686356$

Step 5

The final answer is the combination of both solutions.

$x = 211.04686356, 18.95313643$