Finite Math Examples

$x + 4 x^{2} + 3 x^{3} = 12$ , $- x - 2 x^{2} = - 12$ , $2 x + 2 x^{2} + 3 x^{3} = 8$

Step 1

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

$x \approx 1.19386432$

$- x - 2 x^{2} = - 12$

$2 x + 2 x^{2} + 3 x^{3} = 8$

Step 2

Replace all occurrences of $x$ with $1.19386432$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- x - 2 x^{2} = - 12$ with $1.19386432$ .

$- (1.19386432) - 2 {(1.19386432)}^{2} = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- (1.19386432) - 2 {(1.19386432)}^{2}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Multiply $- 1$ by $1.19386432$ .

$- 1.19386432 - 2 {(1.19386432)}^{2} = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

Step 2.2.1.1.2

Raise $1.19386432$ to the power of $2$ .

$- 1.19386432 - 2 \cdot 1.42531202 = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

Step 2.2.1.1.3

Multiply $- 2$ by $1.42531202$ .

$- 1.19386432 - 2.85062405 = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

$- 1.19386432 - 2.85062405 = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

Step 2.2.1.2

Subtract $2.85062405$ from $- 1.19386432$ .

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$2 x + 2 x^{2} + 3 x^{3} = 8$

Step 2.3

Replace all occurrences of $x$ in $2 x + 2 x^{2} + 3 x^{3} = 8$ with $1.19386432$ .

$2 (1.19386432) + 2 {(1.19386432)}^{2} + 3 {(1.19386432)}^{3} = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $2 (1.19386432) + 2 {(1.19386432)}^{2} + 3 {(1.19386432)}^{3}$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Multiply $2$ by $1.19386432$ .

$2.38772865 + 2 {(1.19386432)}^{2} + 3 {(1.19386432)}^{3} = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 2.4.1.1.2

Raise $1.19386432$ to the power of $2$ .

$2.38772865 + 2 \cdot 1.42531202 + 3 {(1.19386432)}^{3} = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 2.4.1.1.3

Multiply $2$ by $1.42531202$ .

$2.38772865 + 2.85062405 + 3 {(1.19386432)}^{3} = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 2.4.1.1.4

Raise $1.19386432$ to the power of $3$ .

$2.38772865 + 2.85062405 + 3 \cdot 1.70162918 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 2.4.1.1.5

Multiply $3$ by $1.70162918$ .

$2.38772865 + 2.85062405 + 5.10488755 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$2.38772865 + 2.85062405 + 5.10488755 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 2.4.1.2

Simplify by adding numbers.

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Step 2.4.1.2.1

Add $2.38772865$ and $2.85062405$ .

$5.23835271 + 5.10488755 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 2.4.1.2.2

Add $5.23835271$ and $5.10488755$ .

$10.34324026 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$10.34324026 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$10.34324026 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$10.34324026 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

$10.34324026 = 8$

$- 4.04448838 = - 12$

$x \approx 1.19386432$

Step 3

Since $10.34324026 = 8$ is not true, there is no solution.

No solution

Step 4