Pre-Algebra Examples

$600 = 0.0014 x^{2} - 0.1529 x + 5.1$

Step 1

Rewrite the equation as $0.0014 x^{2} - 0.1529 x + 5.1 = 600$ .

$0.0014 x^{2} - 0.1529 x + 5.1 = 600$

Step 2

Subtract $600$ from both sides of the equation.

$0.0014 x^{2} - 0.1529 x + 5.1 - 600 = 0$

Step 3

Subtract $600$ from $5.1$ .

$0.0014 x^{2} - 0.1529 x - 594.9 = 0$

Step 4

Factor $0.0001$ out of $0.0014 x^{2} - 0.1529 x - 594.9$ .

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Step 4.1

Factor $0.0001$ out of $0.0014 x^{2}$ .

$0.0001 (14 x^{2}) - 0.1529 x - 594.9 = 0$

Step 4.2

Factor $0.0001$ out of $- 0.1529 x$ .

$0.0001 (14 x^{2}) + 0.0001 (- 1529 x) - 594.9 = 0$

Step 4.3

Factor $0.0001$ out of $- 594.9$ .

$0.0001 (14 x^{2}) + 0.0001 (- 1529 x) + 0.0001 (- 5949000) = 0$

Step 4.4

Factor $0.0001$ out of $0.0001 (14 x^{2}) + 0.0001 (- 1529 x)$ .

$0.0001 (14 x^{2} - 1529 x) + 0.0001 (- 5949000) = 0$

Step 4.5

Factor $0.0001$ out of $0.0001 (14 x^{2} - 1529 x) + 0.0001 (- 5949000)$ .

$0.0001 (14 x^{2} - 1529 x - 5949000) = 0$

Step 5

Divide each term in $0.0001 (14 x^{2} - 1529 x - 5949000) = 0$ by $0.0001$ and simplify.

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Step 5.1

Divide each term in $0.0001 (14 x^{2} - 1529 x - 5949000) = 0$ by $0.0001$ .

$\frac{0.0001 (14 x^{2} - 1529 x - 5949000)}{0.0001} = \frac{0}{0.0001}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $0.0001$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{0.0001 (14 x^{2} - 1529 x - 5949000)}{0.0001} = \frac{0}{0.0001}$

Step 5.2.1.2

Divide $14 x^{2} - 1529 x - 5949000$ by $1$ .

$14 x^{2} - 1529 x - 5949000 = \frac{0}{0.0001}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $0.0001$ .

$14 x^{2} - 1529 x - 5949000 = 0$

Step 6

Use the quadratic formula to find the solutions.

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

Step 7

Substitute the values $a = 14$ , $b = - 1529$ , and $c = - 5949000$ into the quadratic formula and solve for $x$ .

$\frac{1529 \pm \sqrt{{(- 1529)}^{2} - 4 \cdot (14 \cdot - 5949000)}}{2 \cdot 14}$

Step 8

Simplify.

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Raise $- 1529$ to the power of $2$ .

$x = \frac{1529 \pm \sqrt{2337841 - 4 \cdot 14 \cdot - 5949000}}{2 \cdot 14}$

Step 8.1.2

Multiply $- 4 \cdot 14 \cdot - 5949000$ .

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Step 8.1.2.1

Multiply $- 4$ by $14$ .

$x = \frac{1529 \pm \sqrt{2337841 - 56 \cdot - 5949000}}{2 \cdot 14}$

Step 8.1.2.2

Multiply $- 56$ by $- 5949000$ .

$x = \frac{1529 \pm \sqrt{2337841 + 333144000}}{2 \cdot 14}$

Step 8.1.3

Add $2337841$ and $333144000$ .

$x = \frac{1529 \pm \sqrt{335481841}}{2 \cdot 14}$

Step 8.2

Multiply $2$ by $14$ .

$x = \frac{1529 \pm \sqrt{335481841}}{28}$

Step 9

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Step 9.1

Simplify the numerator.

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Step 9.1.1

Raise $- 1529$ to the power of $2$ .

$x = \frac{1529 \pm \sqrt{2337841 - 4 \cdot 14 \cdot - 5949000}}{2 \cdot 14}$

Step 9.1.2

Multiply $- 4 \cdot 14 \cdot - 5949000$ .

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Step 9.1.2.1

Multiply $- 4$ by $14$ .

$x = \frac{1529 \pm \sqrt{2337841 - 56 \cdot - 5949000}}{2 \cdot 14}$

Step 9.1.2.2

Multiply $- 56$ by $- 5949000$ .

$x = \frac{1529 \pm \sqrt{2337841 + 333144000}}{2 \cdot 14}$

Step 9.1.3

Add $2337841$ and $333144000$ .

$x = \frac{1529 \pm \sqrt{335481841}}{2 \cdot 14}$

Step 9.2

Multiply $2$ by $14$ .

$x = \frac{1529 \pm \sqrt{335481841}}{28}$

Step 9.3

Change the $\pm$ to $+$ .

$x = \frac{1529 + \sqrt{335481841}}{28}$

Step 10

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Step 10.1

Simplify the numerator.

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Step 10.1.1

Raise $- 1529$ to the power of $2$ .

$x = \frac{1529 \pm \sqrt{2337841 - 4 \cdot 14 \cdot - 5949000}}{2 \cdot 14}$

Step 10.1.2

Multiply $- 4 \cdot 14 \cdot - 5949000$ .

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Step 10.1.2.1

Multiply $- 4$ by $14$ .

$x = \frac{1529 \pm \sqrt{2337841 - 56 \cdot - 5949000}}{2 \cdot 14}$

Step 10.1.2.2

Multiply $- 56$ by $- 5949000$ .

$x = \frac{1529 \pm \sqrt{2337841 + 333144000}}{2 \cdot 14}$

Step 10.1.3

Add $2337841$ and $333144000$ .

$x = \frac{1529 \pm \sqrt{335481841}}{2 \cdot 14}$

Step 10.2

Multiply $2$ by $14$ .

$x = \frac{1529 \pm \sqrt{335481841}}{28}$

Step 10.3

Change the $\pm$ to $-$ .

$x = \frac{1529 - \sqrt{335481841}}{28}$

Step 11

The final answer is the combination of both solutions.

$x = \frac{1529 + \sqrt{335481841}}{28}, \frac{1529 - \sqrt{335481841}}{28}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1529 + \sqrt{335481841}}{28}, \frac{1529 - \sqrt{335481841}}{28}$

Decimal Form:

$x = 708.75583503 \dots, - 599.54154932 \dots$