Finite Math Examples

$a^{3} + b = 20$ , $a^{2} + 2 b + 1 = a$

Step 1

Subtract $a^{3}$ from both sides of the equation.

$b = 20 - a^{3}$

$a^{2} + 2 b + 1 = a$

Step 2

Replace all occurrences of $b$ with $20 - a^{3}$ in each equation.

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Step 2.1

Replace all occurrences of $b$ in $a^{2} + 2 b + 1 = a$ with $20 - a^{3}$ .

$a^{2} + 2 (20 - a^{3}) + 1 = a$

$b = 20 - a^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $a^{2} + 2 (20 - a^{3}) + 1$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$a^{2} + 2 \cdot 20 + 2 (- a^{3}) + 1 = a$

$b = 20 - a^{3}$

Step 2.2.1.1.2

Multiply $2$ by $20$ .

$a^{2} + 40 + 2 (- a^{3}) + 1 = a$

$b = 20 - a^{3}$

Step 2.2.1.1.3

Multiply $- 1$ by $2$ .

$a^{2} + 40 - 2 a^{3} + 1 = a$

$b = 20 - a^{3}$

$a^{2} + 40 - 2 a^{3} + 1 = a$

$b = 20 - a^{3}$

Step 2.2.1.2

Add $40$ and $1$ .

$a^{2} - 2 a^{3} + 41 = a$

$b = 20 - a^{3}$

$a^{2} - 2 a^{3} + 41 = a$

$b = 20 - a^{3}$

$a^{2} - 2 a^{3} + 41 = a$

$b = 20 - a^{3}$

$a^{2} - 2 a^{3} + 41 = a$

$b = 20 - a^{3}$

Step 3

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

$a \approx 2.84941511$

$b = 20 - a^{3}$

Step 4