Finite Math Examples

$(x) \cdot (2 x) - 6 x = 4$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$2 x \cdot x - 6 x = 4$

Step 1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.1

Move $x$ .

$2 (x \cdot x) - 6 x = 4$

Step 1.2.2

Multiply $x$ by $x$ .

$2 x^{2} - 6 x = 4$

Step 2

Subtract $4$ from both sides of the equation.

$2 x^{2} - 6 x - 4 = 0$

Step 3

Factor $2$ out of $2 x^{2} - 6 x - 4$ .

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Step 3.1

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 6 x - 4 = 0$

Step 3.2

Factor $2$ out of $- 6 x$ .

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

Step 3.3

Factor $2$ out of $- 4$ .

$2 x^{2} + 2 (- 3 x) + 2 \cdot - 2 = 0$

Step 3.4

Factor $2$ out of $2 x^{2} + 2 (- 3 x)$ .

$2 (x^{2} - 3 x) + 2 \cdot - 2 = 0$

Step 3.5

Factor $2$ out of $2 (x^{2} - 3 x) + 2 \cdot - 2$ .

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

Step 4

Divide each term in $2 (x^{2} - 3 x - 2) = 0$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 (x^{2} - 3 x - 2) = 0$ by $2$ .

$\frac{2 (x^{2} - 3 x - 2)}{2} = \frac{0}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 (x^{2} - 3 x - 2)}{2} = \frac{0}{2}$

Step 4.2.1.2

Divide $x^{2} - 3 x - 2$ by $1$ .

$x^{2} - 3 x - 2 = \frac{0}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $2$ .

$x^{2} - 3 x - 2 = 0$

Step 5

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 6

Substitute the values $a = 1$ , $b = - 3$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (1 \cdot - 2)}}{2 \cdot 1}$

Step 7

Simplify.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 2}}{2 \cdot 1}$

Step 7.1.2

Multiply $- 4 \cdot 1 \cdot - 2$ .

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Step 7.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot - 2}}{2 \cdot 1}$

Step 7.1.2.2

Multiply $- 4$ by $- 2$ .

$x = \frac{3 \pm \sqrt{9 + 8}}{2 \cdot 1}$

Step 7.1.3

Add $9$ and $8$ .

$x = \frac{3 \pm \sqrt{17}}{2 \cdot 1}$

Step 7.2

Multiply $2$ by $1$ .

$x = \frac{3 \pm \sqrt{17}}{2}$

Step 8

The final answer is the combination of both solutions.

$x = \frac{3 + \sqrt{17}}{2}, \frac{3 - \sqrt{17}}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 + \sqrt{17}}{2}, \frac{3 - \sqrt{17}}{2}$

Decimal Form:

$x = 3.56155281 \dots, - 0.56155281 \dots$