Finite Math Examples

$x = 2$ , $a x^{2} + a x + 3 = 0$ , $x^{2} + x + b = 0$ , findab

Step 1

Replace all occurrences of $x$ with $2$ in each equation.

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Step 1.1

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

$a {(2)}^{2} + a (2) + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

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

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

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

$a \cdot 4 + a (2) + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

Step 1.2.1.1.2

Move $4$ to the left of $a$ .

$4 \cdot a + a (2) + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

Step 1.2.1.1.3

Move $2$ to the left of $a$ .

$4 a + 2 a + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

$4 a + 2 a + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

Step 1.2.1.2

Add $4 a$ and $2 a$ .

$6 a + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

$6 a + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

$6 a + 3 = 0$

$x = 2$

$x^{2} + x + b = 0$

Step 1.3

Replace all occurrences of $x$ in $x^{2} + x + b = 0$ with $2$ .

${(2)}^{2} + 2 + b = 0$

$6 a + 3 = 0$

$x = 2$

Step 1.4

Simplify the left side.

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Step 1.4.1

Simplify ${(2)}^{2} + 2 + b$ .

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Step 1.4.1.1

Remove parentheses.

${(2)}^{2} + 2 + b = 0$

$6 a + 3 = 0$

$x = 2$

Step 1.4.1.2

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

$4 + 2 + b = 0$

$6 a + 3 = 0$

$x = 2$

Step 1.4.1.3

Add $4$ and $2$ .

$6 + b = 0$

$6 a + 3 = 0$

$x = 2$

$6 + b = 0$

$6 a + 3 = 0$

$x = 2$

$6 + b = 0$

$6 a + 3 = 0$

$x = 2$

$6 + b = 0$

$6 a + 3 = 0$

$x = 2$

Step 2

Subtract $6$ from both sides of the equation.

$b = - 6$

$6 a + 3 = 0$

$x = 2$

Step 3

Replace all occurrences of $b$ with $- 6$ in each equation.

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Step 3.1

Subtract $3$ from both sides of the equation.

$6 a = - 3$

$b = - 6$

$x = 2$

Step 3.2

Divide each term in $6 a = - 3$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 a = - 3$ by $6$ .

$\frac{6 a}{6} = \frac{- 3}{6}$

$b = - 6$

$x = 2$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 a}{6} = \frac{- 3}{6}$

$b = - 6$

$x = 2$

Step 3.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 3}{6}$

$b = - 6$

$x = 2$

$a = \frac{- 3}{6}$

$b = - 6$

$x = 2$

$a = \frac{- 3}{6}$

$b = - 6$

$x = 2$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $- 3$ and $6$ .

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Step 3.2.3.1.1

Factor $3$ out of $- 3$ .

$a = \frac{3 (- 1)}{6}$

$b = - 6$

$x = 2$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $3$ out of $6$ .

$a = \frac{3 \cdot - 1}{3 \cdot 2}$

$b = - 6$

$x = 2$

Step 3.2.3.1.2.2

Cancel the common factor.

$a = \frac{3 \cdot - 1}{3 \cdot 2}$

$b = - 6$

$x = 2$

Step 3.2.3.1.2.3

Rewrite the expression.

$a = \frac{- 1}{2}$

$b = - 6$

$x = 2$

$a = \frac{- 1}{2}$

$b = - 6$

$x = 2$

$a = \frac{- 1}{2}$

$b = - 6$

$x = 2$

Step 3.2.3.2

Move the negative in front of the fraction.

$a = - \frac{1}{2}$

$b = - 6$

$x = 2$

$a = - \frac{1}{2}$

$b = - 6$

$x = 2$

$a = - \frac{1}{2}$

$b = - 6$

$x = 2$

$a = - \frac{1}{2}$

$b = - 6$

$x = 2$

Step 4

List all of the solutions.

$a = - \frac{1}{2}, b = - 6, x = 2$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}, b = - 6, x = 2$

Decimal Form:

$- 0.5, b = - 6, x = 2$