Pre-Algebra Examples

$1.8395 = x (400 + x)$

Step 1

Rewrite the equation as $x (400 + x) = 1.8395$ .

$x (400 + x) = 1.8395$

Step 2

Simplify $x (400 + x)$ .

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Step 2.1

Apply the distributive property.

$x \cdot 400 + x \cdot x = 1.8395$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $400$ to the left of $x$ .

$400 \cdot x + x \cdot x = 1.8395$

Step 2.2.2

Multiply $x$ by $x$ .

$400 x + x^{2} = 1.8395$

Step 3

Subtract $1.8395$ from both sides of the equation.

$400 x + x^{2} - 1.8395 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 1$ , $b = 400$ , and $c = - 1.8395$ into the quadratic formula and solve for $x$ .

$\frac{- 400 \pm \sqrt{400^{2} - 4 \cdot (1 \cdot - 1.8395)}}{2 \cdot 1}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $400$ to the power of $2$ .

$x = \frac{- 400 \pm \sqrt{160000 - 4 \cdot 1 \cdot - 1.8395}}{2 \cdot 1}$

Step 6.1.2

Multiply $- 4 \cdot 1 \cdot - 1.8395$ .

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Step 6.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 400 \pm \sqrt{160000 - 4 \cdot - 1.8395}}{2 \cdot 1}$

Step 6.1.2.2

Multiply $- 4$ by $- 1.8395$ .

$x = \frac{- 400 \pm \sqrt{160000 + 7.358}}{2 \cdot 1}$

Step 6.1.3

Add $160000$ and $7.358$ .

$x = \frac{- 400 \pm \sqrt{160007.358}}{2 \cdot 1}$

Step 6.2

Multiply $2$ by $1$ .

$x = \frac{- 400 \pm \sqrt{160007.358}}{2}$

Step 7

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

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $400$ to the power of $2$ .

$x = \frac{- 400 \pm \sqrt{160000 - 4 \cdot 1 \cdot - 1.8395}}{2 \cdot 1}$

Step 7.1.2

Multiply $- 4 \cdot 1 \cdot - 1.8395$ .

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Step 7.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 400 \pm \sqrt{160000 - 4 \cdot - 1.8395}}{2 \cdot 1}$

Step 7.1.2.2

Multiply $- 4$ by $- 1.8395$ .

$x = \frac{- 400 \pm \sqrt{160000 + 7.358}}{2 \cdot 1}$

Step 7.1.3

Add $160000$ and $7.358$ .

$x = \frac{- 400 \pm \sqrt{160007.358}}{2 \cdot 1}$

Step 7.2

Multiply $2$ by $1$ .

$x = \frac{- 400 \pm \sqrt{160007.358}}{2}$

Step 7.3

Change the $\pm$ to $+$ .

$x = \frac{- 400 + \sqrt{160007.358}}{2}$

Step 7.4

Rewrite $- 400$ as $- 1 (400)$ .

$x = \frac{- 1 \cdot 400 + \sqrt{160007.358}}{2}$

Step 7.5

Factor $- 1$ out of $\sqrt{160007.358}$ .

$x = \frac{- 1 \cdot 400 - 1 (- \sqrt{160007.358})}{2}$

Step 7.6

Factor $- 1$ out of $- 1 (400) - 1 (- \sqrt{160007.358})$ .

$x = \frac{- 1 (400 - \sqrt{160007.358})}{2}$

Step 7.7

Move the negative in front of the fraction.

$x = - \frac{400 - \sqrt{160007.358}}{2}$

Step 8

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

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Raise $400$ to the power of $2$ .

$x = \frac{- 400 \pm \sqrt{160000 - 4 \cdot 1 \cdot - 1.8395}}{2 \cdot 1}$

Step 8.1.2

Multiply $- 4 \cdot 1 \cdot - 1.8395$ .

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Step 8.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 400 \pm \sqrt{160000 - 4 \cdot - 1.8395}}{2 \cdot 1}$

Step 8.1.2.2

Multiply $- 4$ by $- 1.8395$ .

$x = \frac{- 400 \pm \sqrt{160000 + 7.358}}{2 \cdot 1}$

Step 8.1.3

Add $160000$ and $7.358$ .

$x = \frac{- 400 \pm \sqrt{160007.358}}{2 \cdot 1}$

Step 8.2

Multiply $2$ by $1$ .

$x = \frac{- 400 \pm \sqrt{160007.358}}{2}$

Step 8.3

Change the $\pm$ to $-$ .

$x = \frac{- 400 - \sqrt{160007.358}}{2}$

Step 8.4

Rewrite $- 400$ as $- 1 (400)$ .

$x = \frac{- 1 \cdot 400 - \sqrt{160007.358}}{2}$

Step 8.5

Factor $- 1$ out of $- \sqrt{160007.358}$ .

$x = \frac{- 1 \cdot 400 - (\sqrt{160007.358})}{2}$

Step 8.6

Factor $- 1$ out of $- 1 (400) - (\sqrt{160007.358})$ .

$x = \frac{- 1 (400 + \sqrt{160007.358})}{2}$

Step 8.7

Move the negative in front of the fraction.

$x = - \frac{400 + \sqrt{160007.358}}{2}$

Step 9

The final answer is the combination of both solutions.

$x = - \frac{400 - \sqrt{160007.358}}{2}, - \frac{400 + \sqrt{160007.358}}{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{400 - \sqrt{160007.358}}{2}, - \frac{400 + \sqrt{160007.358}}{2}$

Decimal Form:

$x = 0.00459869 \dots, - 400.00459869 \dots$