Finite Math Examples

x + 2 x^{2} + 3 x^{3} - x^{4} = 0

$x + 2 x^{2} + 3 x^{3} - x^{4} = 0$ ,

x - x^{3} - x^{4} = 2

$x - x^{3} - x^{4} = 2$ ,

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 1

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

x \approx 0, 3.62736508

$x \approx 0, 3.62736508$

x - x^{3} - x^{4} = 2

$x - x^{3} - x^{4} = 2$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2

Solve the system

x = 0, x - x^{3} - x^{4} = 2, 3 x - x^{4} = 4

$x = 0, x - x^{3} - x^{4} = 2, 3 x - x^{4} = 4$ .

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Step 2.1

Replace all occurrences of

x

$x$ with

0

$0$ in each equation.

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Step 2.1.1

Replace all occurrences of

x

$x$ in

x - x^{3} - x^{4} = 2

$x - x^{3} - x^{4} = 2$ with

0

$0$ .

(0) - {(0)}^{3} - {(0)}^{4} = 2

$(0) - {(0)}^{3} - {(0)}^{4} = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Simplify

(0) - {(0)}^{3} - {(0)}^{4}

$(0) - {(0)}^{3} - {(0)}^{4}$ .

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Step 2.1.2.1.1

Simplify each term.

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Step 2.1.2.1.1.1

Raising

0

$0$ to any positive power yields

0

$0$ .

0 - 0 - {(0)}^{4} = 2

$0 - 0 - {(0)}^{4} = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2.1.2.1.1.2

Multiply

- 1

$- 1$ by

0

$0$ .

0 + 0 - {(0)}^{4} = 2

$0 + 0 - {(0)}^{4} = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2.1.2.1.1.3

Raising

0

$0$ to any positive power yields

0

$0$ .

0 + 0 - 0 = 2

$0 + 0 - 0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2.1.2.1.1.4

Multiply

- 1

$- 1$ by

0

$0$ .

0 + 0 + 0 = 2

$0 + 0 + 0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

0 + 0 + 0 = 2

$0 + 0 + 0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2.1.2.1.2

Simplify by adding numbers.

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Step 2.1.2.1.2.1

Add

0

$0$ and

0

$0$ .

0 + 0 = 2

$0 + 0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2.1.2.1.2.2

Add

0

$0$ and

0

$0$ .

0 = 2

$0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

3 x - x^{4} = 4

$3 x - x^{4} = 4$

Step 2.1.3

Replace all occurrences of

x

$x$ in

3 x - x^{4} = 4

$3 x - x^{4} = 4$ with

0

$0$ .

3 (0) - {(0)}^{4} = 4

$3 (0) - {(0)}^{4} = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

Step 2.1.4

Simplify the left side.

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Step 2.1.4.1

Simplify

3 (0) - {(0)}^{4}

$3 (0) - {(0)}^{4}$ .

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Step 2.1.4.1.1

Simplify each term.

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Step 2.1.4.1.1.1

Multiply

3

$3$ by

0

$0$ .

0 - {(0)}^{4} = 4

$0 - {(0)}^{4} = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

Step 2.1.4.1.1.2

Raising

0

$0$ to any positive power yields

0

$0$ .

0 - 0 = 4

$0 - 0 = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

Step 2.1.4.1.1.3

Multiply

- 1

$- 1$ by

0

$0$ .

0 + 0 = 4

$0 + 0 = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

0 + 0 = 4

$0 + 0 = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

Step 2.1.4.1.2

Add

0

$0$ and

0

$0$ .

0 = 4

$0 = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

0 = 4

$0 = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

0 = 4

$0 = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

0 = 4

$0 = 4$

0 = 2

$0 = 2$

x = 0

$x = 0$

Step 2.2

Since

0 = 4

$0 = 4$ is not true, there is no solution.

No solution

No solution

Step 3

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$