Finite Math Examples

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

Step 1

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

$x \approx 0, 3.62736508$

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

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

Step 2

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

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Step 2.1

Replace all occurrences of $x$ with $0$ in each equation.

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Step 2.1.1

Replace all occurrences of $x$ in $x - x^{3} - x^{4} = 2$ with $0$ .

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

$x = 0$

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

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

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

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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 $0$ to any positive power yields $0$ .

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

$x = 0$

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

Step 2.1.2.1.1.2

Multiply $- 1$ by $0$ .

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

$x = 0$

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

Step 2.1.2.1.1.3

Raising $0$ to any positive power yields $0$ .

$0 + 0 - 0 = 2$

$x = 0$

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

Step 2.1.2.1.1.4

Multiply $- 1$ by $0$ .

$0 + 0 + 0 = 2$

$x = 0$

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

$0 + 0 + 0 = 2$

$x = 0$

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

Step 2.1.2.1.2

Simplify by adding numbers.

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Step 2.1.2.1.2.1

Add $0$ and $0$ .

$0 + 0 = 2$

$x = 0$

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

Step 2.1.2.1.2.2

Add $0$ and $0$ .

$0 = 2$

$x = 0$

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

$0 = 2$

$x = 0$

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

$0 = 2$

$x = 0$

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

$0 = 2$

$x = 0$

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

Step 2.1.3

Replace all occurrences of $x$ in $3 x - x^{4} = 4$ with $0$ .

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

$0 = 2$

$x = 0$

Step 2.1.4

Simplify the left side.

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Step 2.1.4.1

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

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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 $3$ by $0$ .

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

$0 = 2$

$x = 0$

Step 2.1.4.1.1.2

Raising $0$ to any positive power yields $0$ .

$0 - 0 = 4$

$0 = 2$

$x = 0$

Step 2.1.4.1.1.3

Multiply $- 1$ by $0$ .

$0 + 0 = 4$

$0 = 2$

$x = 0$

$0 + 0 = 4$

$0 = 2$

$x = 0$

Step 2.1.4.1.2

Add $0$ and $0$ .

$0 = 4$

$0 = 2$

$x = 0$

$0 = 4$

$0 = 2$

$x = 0$

$0 = 4$

$0 = 2$

$x = 0$

$0 = 4$

$0 = 2$

$x = 0$

Step 2.2

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

No solution

Step 3