Finite Math Examples

$3 x^{2} + 12 x = 33$

Step 1

Divide each term in $3 x^{2} + 12 x = 33$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 x^{2} + 12 x = 33$ by $3$ .

$\frac{3 x^{2}}{3} + \frac{12 x}{3} = \frac{33}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Cancel the common factor of $3$ .

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Step 1.2.1.1.1

Cancel the common factor.

$\frac{3 x^{2}}{3} + \frac{12 x}{3} = \frac{33}{3}$

Step 1.2.1.1.2

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{12 x}{3} = \frac{33}{3}$

Step 1.2.1.2

Cancel the common factor of $12$ and $3$ .

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Step 1.2.1.2.1

Factor $3$ out of $12 x$ .

$x^{2} + \frac{3 (4 x)}{3} = \frac{33}{3}$

Step 1.2.1.2.2

Cancel the common factors.

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Step 1.2.1.2.2.1

Factor $3$ out of $3$ .

$x^{2} + \frac{3 (4 x)}{3 (1)} = \frac{33}{3}$

Step 1.2.1.2.2.2

Cancel the common factor.

$x^{2} + \frac{3 (4 x)}{3 \cdot 1} = \frac{33}{3}$

Step 1.2.1.2.2.3

Rewrite the expression.

$x^{2} + \frac{4 x}{1} = \frac{33}{3}$

Step 1.2.1.2.2.4

Divide $4 x$ by $1$ .

$x^{2} + 4 x = \frac{33}{3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $33$ by $3$ .

$x^{2} + 4 x = 11$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(2)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 4 x + {(2)}^{2} = 11 + {(2)}^{2}$

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

$x^{2} + 4 x + 4 = 11 + {(2)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $11 + {(2)}^{2}$ .

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Step 4.2.1.1

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

$x^{2} + 4 x + 4 = 11 + 4$

Step 4.2.1.2

Add $11$ and $4$ .

$x^{2} + 4 x + 4 = 15$

Step 5

Factor the perfect trinomial square into ${(x + 2)}^{2}$ .

${(x + 2)}^{2} = 15$

Step 6

Solve the equation for $x$ .

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Step 6.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 2 = \pm \sqrt{15}$

Step 6.2

Subtract $2$ from both sides of the equation.

$x = \pm \sqrt{15} - 2$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{15} - 2$

Decimal Form:

$x = 1.87298334 \dots, - 5.87298334 \dots$