Finite Math Examples

$10 x + 6 x^{2} - 9 x^{3} = 21$ , $15 x - 4 x^{2} + 9 x^{3} = - 24$ , $- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 1

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 1.37516967$

$15 x - 4 x^{2} + 9 x^{3} = - 24$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2

Replace all occurrences of $x$ with $- 1.37516967$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $15 x - 4 x^{2} + 9 x^{3} = - 24$ with $- 1.37516967$ .

$15 (- 1.37516967) - 4 {(- 1.37516967)}^{2} + 9 {(- 1.37516967)}^{3} = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $15 (- 1.37516967) - 4 {(- 1.37516967)}^{2} + 9 {(- 1.37516967)}^{3}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Multiply $15$ by $- 1.37516967$ .

$- 20.62754515 - 4 {(- 1.37516967)}^{2} + 9 {(- 1.37516967)}^{3} = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.2.1.1.2

Raise $- 1.37516967$ to the power of $2$ .

$- 20.62754515 - 4 \cdot 1.89109164 + 9 {(- 1.37516967)}^{3} = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.2.1.1.3

Multiply $- 4$ by $1.89109164$ .

$- 20.62754515 - 7.56436656 + 9 {(- 1.37516967)}^{3} = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.2.1.1.4

Raise $- 1.37516967$ to the power of $3$ .

$- 20.62754515 - 7.56436656 + 9 \cdot - 2.60057188 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.2.1.1.5

Multiply $9$ by $- 2.60057188$ .

$- 20.62754515 - 7.56436656 - 23.40514692 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

$- 20.62754515 - 7.56436656 - 23.40514692 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.2.1.2

Simplify by subtracting numbers.

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Step 2.2.1.2.1

Subtract $7.56436656$ from $- 20.62754515$ .

$- 28.19191171 - 23.40514692 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.2.1.2.2

Subtract $23.40514692$ from $- 28.19191171$ .

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$- 10 + 3 x^{2} - 4 x^{3} = 20$

Step 2.3

Replace all occurrences of $x$ in $- 10 + 3 x^{2} - 4 x^{3} = 20$ with $- 1.37516967$ .

$- 10 + 3 {(- 1.37516967)}^{2} - 4 {(- 1.37516967)}^{3} = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $- 10 + 3 {(- 1.37516967)}^{2} - 4 {(- 1.37516967)}^{3}$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Raise $- 1.37516967$ to the power of $2$ .

$- 10 + 3 \cdot 1.89109164 - 4 {(- 1.37516967)}^{3} = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

Step 2.4.1.1.2

Multiply $3$ by $1.89109164$ .

$- 10 + 5.67327492 - 4 {(- 1.37516967)}^{3} = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

Step 2.4.1.1.3

Raise $- 1.37516967$ to the power of $3$ .

$- 10 + 5.67327492 - 4 \cdot - 2.60057188 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

Step 2.4.1.1.4

Multiply $- 4$ by $- 2.60057188$ .

$- 10 + 5.67327492 + 10.40228752 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$- 10 + 5.67327492 + 10.40228752 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

Step 2.4.1.2

Simplify by adding numbers.

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Step 2.4.1.2.1

Add $- 10$ and $5.67327492$ .

$- 4.32672507 + 10.40228752 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

Step 2.4.1.2.2

Add $- 4.32672507$ and $10.40228752$ .

$6.07556244 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$6.07556244 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$6.07556244 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$6.07556244 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

$6.07556244 = 20$

$- 51.59705864 = - 24$

$x \approx - 1.37516967$

Step 3

Since $6.07556244 = 20$ is not true, there is no solution.

No solution

Step 4