Finite Math Examples

$l (25) = - 2.318 + 0.2356 x - 0.002674 x^{2}$

Step 1

Rewrite the equation as $- 2.318 + 0.2356 x - 0.002674 x^{2} = l (25)$ .

$- 2.318 + 0.2356 x - 0.002674 x^{2} = l (25)$

Step 2

Move $25$ to the left of $l$ .

$- 2.318 + 0.2356 x - 0.002674 x^{2} = 25 l$

Step 3

Subtract $25 l$ from both sides of the equation.

$- 2.318 + 0.2356 x - 0.002674 x^{2} - 25 l = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = - 0.002674$ , $b = 0.2356$ , and $c = - 2.318 - 25 l$ into the quadratic formula and solve for $x$ .

$\frac{- 0.2356 \pm \sqrt{{0.2356}^{2} - 4 \cdot (- 0.002674 \cdot (- 2.318 - 25 l))}}{2 \cdot - 0.002674}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $0.2356$ to the power of $2$ .

$x = \frac{- 0.2356 \pm \sqrt{0.05550736 - 4 \cdot - 0.002674 \cdot (- 2.318 - 25 l)}}{2 \cdot - 0.002674}$

Step 6.1.2

Multiply $- 4$ by $- 0.002674$ .

$x = \frac{- 0.2356 \pm \sqrt{0.05550736 + 0.010696 \cdot (- 2.318 - 25 l)}}{2 \cdot - 0.002674}$

Step 6.1.3

Apply the distributive property.

$x = \frac{- 0.2356 \pm \sqrt{0.05550736 + 0.010696 \cdot - 2.318 + 0.010696 (- 25 l)}}{2 \cdot - 0.002674}$

Step 6.1.4

Multiply $0.010696$ by $- 2.318$ .

$x = \frac{- 0.2356 \pm \sqrt{0.05550736 - 0.02479332 + 0.010696 (- 25 l)}}{2 \cdot - 0.002674}$

Step 6.1.5

Multiply $- 25$ by $0.010696$ .

$x = \frac{- 0.2356 \pm \sqrt{0.05550736 - 0.02479332 - 0.2674 l}}{2 \cdot - 0.002674}$

Step 6.1.6

Subtract $0.02479332$ from $0.05550736$ .

$x = \frac{- 0.2356 \pm \sqrt{0.03071403 - 0.2674 l}}{2 \cdot - 0.002674}$

Step 6.1.7

Factor $0.00000001$ out of $0.03071403 - 0.2674 l$ .

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Step 6.1.7.1

Factor $0.00000001$ out of $0.03071403$ .

$x = \frac{- 0.2356 \pm \sqrt{0.00000001 (1919627) - 0.2674 l}}{2 \cdot - 0.002674}$

Step 6.1.7.2

Factor $0.00000001$ out of $- 0.2674 l$ .

$x = \frac{- 0.2356 \pm \sqrt{0.00000001 (1919627) + 0.00000001 (- 16712500 l)}}{2 \cdot - 0.002674}$

Step 6.1.7.3

Factor $0.00000001$ out of $0.00000001 (1919627) + 0.00000001 (- 16712500 l)$ .

$x = \frac{- 0.2356 \pm \sqrt{0.00000001 (1919627 - 16712500 l)}}{2 \cdot - 0.002674}$

Step 6.1.8

Rewrite $0.00000001 (1919627 - 16712500 l)$ as ${({0.01124682}^{2})}^{2} (1919627 - 16712500 l)$ .

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Step 6.1.8.1

Rewrite $0.00000001$ as ${0.00012649}^{2}$ .

$x = \frac{- 0.2356 \pm \sqrt{{0.00012649}^{2} (1919627 - 16712500 l)}}{2 \cdot - 0.002674}$

Step 6.1.8.2

Rewrite $0.00012649$ as ${0.01124682}^{2}$ .

$x = \frac{- 0.2356 \pm \sqrt{{({0.01124682}^{2})}^{2} (1919627 - 16712500 l)}}{2 \cdot - 0.002674}$

Step 6.1.9

Pull terms out from under the radical.

$x = \frac{- 0.2356 \pm {0.01124682}^{2} \sqrt{1919627 - 16712500 l}}{2 \cdot - 0.002674}$

Step 6.1.10

Raise $0.01124682$ to the power of $2$ .

$x = \frac{- 0.2356 \pm 0.00012649 \sqrt{1919627 - 16712500 l}}{2 \cdot - 0.002674}$

Step 6.2

Multiply $2$ by $- 0.002674$ .

$x = \frac{- 0.2356 \pm 0.00012649 \sqrt{1919627 - 16712500 l}}{- 0.005348}$

Step 6.3

Simplify $\frac{- 0.2356 \pm 0.00012649 \sqrt{1919627 - 16712500 l}}{- 0.005348}$ .

$x = \frac{58900 \pm 31.6227766 \sqrt{1919627 - 16712500 l}}{1337}$

Step 7

The final answer is the combination of both solutions.

$x = \frac{58900 + 31.6227766 \sqrt{1919627 - 16712500 l}}{1337}$

$x = \frac{58900 - 31.6227766 \sqrt{1919627 - 16712500 l}}{1337}$