Pre-Algebra Examples

$0.164 x^{2} + 0.004 x - 0.493 = 0$

Step 1

Factor $0.001$ out of $0.164 x^{2} + 0.004 x - 0.493$ .

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Step 1.1

Factor $0.001$ out of $0.164 x^{2}$ .

$0.001 (164 x^{2}) + 0.004 x - 0.493 = 0$

Step 1.2

Factor $0.001$ out of $0.004 x$ .

$0.001 (164 x^{2}) + 0.001 (4 x) - 0.493 = 0$

Step 1.3

Factor $0.001$ out of $- 0.493$ .

$0.001 (164 x^{2}) + 0.001 (4 x) + 0.001 (- 493) = 0$

Step 1.4

Factor $0.001$ out of $0.001 (164 x^{2}) + 0.001 (4 x)$ .

$0.001 (164 x^{2} + 4 x) + 0.001 (- 493) = 0$

Step 1.5

Factor $0.001$ out of $0.001 (164 x^{2} + 4 x) + 0.001 (- 493)$ .

$0.001 (164 x^{2} + 4 x - 493) = 0$

Step 2

Divide each term in $0.001 (164 x^{2} + 4 x - 493) = 0$ by $0.001$ and simplify.

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Step 2.1

Divide each term in $0.001 (164 x^{2} + 4 x - 493) = 0$ by $0.001$ .

$\frac{0.001 (164 x^{2} + 4 x - 493)}{0.001} = \frac{0}{0.001}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.001$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.001 (164 x^{2} + 4 x - 493)}{0.001} = \frac{0}{0.001}$

Step 2.2.1.2

Divide $164 x^{2} + 4 x - 493$ by $1$ .

$164 x^{2} + 4 x - 493 = \frac{0}{0.001}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $0.001$ .

$164 x^{2} + 4 x - 493 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 164$ , $b = 4$ , and $c = - 493$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (164 \cdot - 493)}}{2 \cdot 164}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 164 \cdot - 493}}{2 \cdot 164}$

Step 5.1.2

Multiply $- 4 \cdot 164 \cdot - 493$ .

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Step 5.1.2.1

Multiply $- 4$ by $164$ .

$x = \frac{- 4 \pm \sqrt{16 - 656 \cdot - 493}}{2 \cdot 164}$

Step 5.1.2.2

Multiply $- 656$ by $- 493$ .

$x = \frac{- 4 \pm \sqrt{16 + 323408}}{2 \cdot 164}$

Step 5.1.3

Add $16$ and $323408$ .

$x = \frac{- 4 \pm \sqrt{323424}}{2 \cdot 164}$

Step 5.1.4

Rewrite $323424$ as $12^{2} \cdot 2246$ .

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Step 5.1.4.1

Factor $144$ out of $323424$ .

$x = \frac{- 4 \pm \sqrt{144 (2246)}}{2 \cdot 164}$

Step 5.1.4.2

Rewrite $144$ as $12^{2}$ .

$x = \frac{- 4 \pm \sqrt{12^{2} \cdot 2246}}{2 \cdot 164}$

Step 5.1.5

Pull terms out from under the radical.

$x = \frac{- 4 \pm 12 \sqrt{2246}}{2 \cdot 164}$

Step 5.2

Multiply $2$ by $164$ .

$x = \frac{- 4 \pm 12 \sqrt{2246}}{328}$

Step 5.3

Simplify $\frac{- 4 \pm 12 \sqrt{2246}}{328}$ .

$x = \frac{- 1 \pm 3 \sqrt{2246}}{82}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{1 - 3 \sqrt{2246}}{82}, - \frac{1 + 3 \sqrt{2246}}{82}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1 - 3 \sqrt{2246}}{82}, - \frac{1 + 3 \sqrt{2246}}{82}$

Decimal Form:

$x = 1.72165789 \dots, - 1.74604813 \dots$