Finite Math Examples

$(8 x - 2 x) (15 - 2 x) = 44$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $(8 x - 2 x) (15 - 2 x)$ .

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Step 1.1.1.1

Simplify terms.

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Step 1.1.1.1.1

Subtract $2 x$ from $8 x$ .

$6 x (15 - 2 x) = 44$

Step 1.1.1.1.2

Apply the distributive property.

$6 x \cdot 15 + 6 x (- 2 x) = 44$

Step 1.1.1.1.3

Simplify the expression.

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Step 1.1.1.1.3.1

Multiply $15$ by $6$ .

$90 x + 6 x (- 2 x) = 44$

Step 1.1.1.1.3.2

Rewrite using the commutative property of multiplication.

$90 x + 6 \cdot - 2 x \cdot x = 44$

Step 1.1.1.2

Simplify each term.

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Step 1.1.1.2.1

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

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Step 1.1.1.2.1.1

Move $x$ .

$90 x + 6 \cdot - 2 (x \cdot x) = 44$

Step 1.1.1.2.1.2

Multiply $x$ by $x$ .

$90 x + 6 \cdot - 2 x^{2} = 44$

Step 1.1.1.2.2

Multiply $6$ by $- 2$ .

$90 x - 12 x^{2} = 44$

Step 1.2

Subtract $44$ from both sides of the equation.

$90 x - 12 x^{2} - 44 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = - 12$ , $b = 90$ , and $c = - 44$ into the quadratic formula and solve for $x$ .

$\frac{- 90 \pm \sqrt{90^{2} - 4 \cdot (- 12 \cdot - 44)}}{2 \cdot - 12}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $90$ to the power of $2$ .

$x = \frac{- 90 \pm \sqrt{8100 - 4 \cdot - 12 \cdot - 44}}{2 \cdot - 12}$

Step 4.1.2

Multiply $- 4 \cdot - 12 \cdot - 44$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 12$ .

$x = \frac{- 90 \pm \sqrt{8100 + 48 \cdot - 44}}{2 \cdot - 12}$

Step 4.1.2.2

Multiply $48$ by $- 44$ .

$x = \frac{- 90 \pm \sqrt{8100 - 2112}}{2 \cdot - 12}$

Step 4.1.3

Subtract $2112$ from $8100$ .

$x = \frac{- 90 \pm \sqrt{5988}}{2 \cdot - 12}$

Step 4.1.4

Rewrite $5988$ as $2^{2} \cdot 1497$ .

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Step 4.1.4.1

Factor $4$ out of $5988$ .

$x = \frac{- 90 \pm \sqrt{4 (1497)}}{2 \cdot - 12}$

Step 4.1.4.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 90 \pm \sqrt{2^{2} \cdot 1497}}{2 \cdot - 12}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{- 90 \pm 2 \sqrt{1497}}{2 \cdot - 12}$

Step 4.2

Multiply $2$ by $- 12$ .

$x = \frac{- 90 \pm 2 \sqrt{1497}}{- 24}$

Step 4.3

Simplify $\frac{- 90 \pm 2 \sqrt{1497}}{- 24}$ .

$x = \frac{45 \pm \sqrt{1497}}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{45 \pm \sqrt{1497}}{12}$

Decimal Form:

$x = 6.97425702 \dots, 0.52574297 \dots$