Pre-Algebra Examples

$0.07 x + 0.06 x (18000 - x) = 1160$

Step 1

Simplify $0.07 x + 0.06 x (18000 - x)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$0.07 x + 0.06 x \cdot 18000 + 0.06 x (- x) = 1160$

Step 1.1.2

Multiply $18000$ by $0.06$ .

$0.07 x + 1080 x + 0.06 x (- x) = 1160$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$0.07 x + 1080 x + 0.06 \cdot - 1 x \cdot x = 1160$

Step 1.1.4

Simplify each term.

Tap for more steps...

Step 1.1.4.1

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

Tap for more steps...

Step 1.1.4.1.1

Move $x$ .

$0.07 x + 1080 x + 0.06 \cdot - 1 (x \cdot x) = 1160$

Step 1.1.4.1.2

Multiply $x$ by $x$ .

$0.07 x + 1080 x + 0.06 \cdot - 1 x^{2} = 1160$

Step 1.1.4.2

Multiply $0.06$ by $- 1$ .

$0.07 x + 1080 x - 0.06 x^{2} = 1160$

Step 1.2

Add $0.07 x$ and $1080 x$ .

$1080.07 x - 0.06 x^{2} = 1160$

Step 2

Subtract $1160$ from both sides of the equation.

$1080.07 x - 0.06 x^{2} - 1160 = 0$

Step 3

Factor $- 0.01$ out of $1080.07 x - 0.06 x^{2} - 1160$ .

Tap for more steps...

Step 3.1

Reorder $1080.07 x$ and $- 0.06 x^{2}$ .

$- 0.06 x^{2} + 1080.07 x - 1160 = 0$

Step 3.2

Factor $- 0.01$ out of $- 0.06 x^{2}$ .

$- 0.01 (6 x^{2}) + 1080.07 x - 1160 = 0$

Step 3.3

Factor $- 0.01$ out of $1080.07 x$ .

$- 0.01 (6 x^{2}) - 0.01 (- 108007 x) - 1160 = 0$

Step 3.4

Factor $- 0.01$ out of $- 1160$ .

$- 0.01 (6 x^{2}) - 0.01 (- 108007 x) - 0.01 \cdot 116000 = 0$

Step 3.5

Factor $- 0.01$ out of $- 0.01 (6 x^{2}) - 0.01 (- 108007 x)$ .

$- 0.01 (6 x^{2} - 108007 x) - 0.01 \cdot 116000 = 0$

Step 3.6

Factor $- 0.01$ out of $- 0.01 (6 x^{2} - 108007 x) - 0.01 (116000)$ .

$- 0.01 (6 x^{2} - 108007 x + 116000) = 0$

Step 4

Divide each term in $- 0.01 (6 x^{2} - 108007 x + 116000) = 0$ by $- 0.01$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- 0.01 (6 x^{2} - 108007 x + 116000) = 0$ by $- 0.01$ .

$\frac{- 0.01 (6 x^{2} - 108007 x + 116000)}{- 0.01} = \frac{0}{- 0.01}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 0.01$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 0.01 (6 x^{2} - 108007 x + 116000)}{- 0.01} = \frac{0}{- 0.01}$

Step 4.2.1.2

Divide $6 x^{2} - 108007 x + 116000$ by $1$ .

$6 x^{2} - 108007 x + 116000 = \frac{0}{- 0.01}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $0$ by $- 0.01$ .

$6 x^{2} - 108007 x + 116000 = 0$

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 $a = 6$ , $b = - 108007$ , and $c = 116000$ into the quadratic formula and solve for $x$ .

$\frac{108007 \pm \sqrt{{(- 108007)}^{2} - 4 \cdot (6 \cdot 116000)}}{2 \cdot 6}$

Step 7

Simplify.

Tap for more steps...

Step 7.1

Simplify the numerator.

Tap for more steps...

Step 7.1.1

Raise $- 108007$ to the power of $2$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 4 \cdot 6 \cdot 116000}}{2 \cdot 6}$

Step 7.1.2

Multiply $- 4 \cdot 6 \cdot 116000$ .

Tap for more steps...

Step 7.1.2.1

Multiply $- 4$ by $6$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 24 \cdot 116000}}{2 \cdot 6}$

Step 7.1.2.2

Multiply $- 24$ by $116000$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 2784000}}{2 \cdot 6}$

Step 7.1.3

Subtract $2784000$ from $11665512049$ .

$x = \frac{108007 \pm \sqrt{11662728049}}{2 \cdot 6}$

Step 7.2

Multiply $2$ by $6$ .

$x = \frac{108007 \pm \sqrt{11662728049}}{12}$

Step 8

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

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

Raise $- 108007$ to the power of $2$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 4 \cdot 6 \cdot 116000}}{2 \cdot 6}$

Step 8.1.2

Multiply $- 4 \cdot 6 \cdot 116000$ .

Tap for more steps...

Step 8.1.2.1

Multiply $- 4$ by $6$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 24 \cdot 116000}}{2 \cdot 6}$

Step 8.1.2.2

Multiply $- 24$ by $116000$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 2784000}}{2 \cdot 6}$

Step 8.1.3

Subtract $2784000$ from $11665512049$ .

$x = \frac{108007 \pm \sqrt{11662728049}}{2 \cdot 6}$

Step 8.2

Multiply $2$ by $6$ .

$x = \frac{108007 \pm \sqrt{11662728049}}{12}$

Step 8.3

Change the $\pm$ to $+$ .

$x = \frac{108007 + \sqrt{11662728049}}{12}$

Step 9

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

Tap for more steps...

Step 9.1

Simplify the numerator.

Tap for more steps...

Step 9.1.1

Raise $- 108007$ to the power of $2$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 4 \cdot 6 \cdot 116000}}{2 \cdot 6}$

Step 9.1.2

Multiply $- 4 \cdot 6 \cdot 116000$ .

Tap for more steps...

Step 9.1.2.1

Multiply $- 4$ by $6$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 24 \cdot 116000}}{2 \cdot 6}$

Step 9.1.2.2

Multiply $- 24$ by $116000$ .

$x = \frac{108007 \pm \sqrt{11665512049 - 2784000}}{2 \cdot 6}$

Step 9.1.3

Subtract $2784000$ from $11665512049$ .

$x = \frac{108007 \pm \sqrt{11662728049}}{2 \cdot 6}$

Step 9.2

Multiply $2$ by $6$ .

$x = \frac{108007 \pm \sqrt{11662728049}}{12}$

Step 9.3

Change the $\pm$ to $-$ .

$x = \frac{108007 - \sqrt{11662728049}}{12}$

Step 10

The final answer is the combination of both solutions.

$x = \frac{108007 + \sqrt{11662728049}}{12}, \frac{108007 - \sqrt{11662728049}}{12}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$x = \frac{108007 + \sqrt{11662728049}}{12}, \frac{108007 - \sqrt{11662728049}}{12}$

Decimal Form:

$x = 18000.09259811 \dots, 1.07406854 \dots$