Solve 3000/x+3000/xdiv1.2x=1100

$$\frac { 3000 } { x } + \frac { 3000 } { x } \div 1.2 x = 1100$$

Solve for x

$$x = -\frac{15}{7} = -2\frac{1}{7} \approx -2.142857143$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3000+\frac{5}{6}x\times \frac{3000}{x}x=1100x$$

Multiply x and x to get x^{2}.

$$3000+\frac{5}{6}x^{2}\times \frac{3000}{x}=1100x$$

Multiply \frac{5}{6} times \frac{3000}{x} by multiplying numerator times numerator and denominator times denominator.

$$3000+\frac{5\times 3000}{6x}x^{2}=1100x$$

Cancel out 6 in both numerator and denominator.

$$3000+\frac{5\times 500}{x}x^{2}=1100x$$

Multiply 5 and 500 to get 2500.

$$3000+\frac{2500}{x}x^{2}=1100x$$

Express \frac{2500}{x}x^{2} as a single fraction.

$$3000+\frac{2500x^{2}}{x}=1100x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3000 times \frac{x}{x}.

$$\frac{3000x}{x}+\frac{2500x^{2}}{x}=1100x$$

Since \frac{3000x}{x} and \frac{2500x^{2}}{x} have the same denominator, add them by adding their numerators.

$$\frac{3000x+2500x^{2}}{x}=1100x$$

Subtract 1100x from both sides.

$$\frac{3000x+2500x^{2}}{x}-1100x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -1100x times \frac{x}{x}.

$$\frac{3000x+2500x^{2}}{x}+\frac{-1100xx}{x}=0$$

Since \frac{3000x+2500x^{2}}{x} and \frac{-1100xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{3000x+2500x^{2}-1100xx}{x}=0$$

Do the multiplications in 3000x+2500x^{2}-1100xx.

$$\frac{3000x+2500x^{2}-1100x^{2}}{x}=0$$

Combine like terms in 3000x+2500x^{2}-1100x^{2}.

$$\frac{3000x+1400x^{2}}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3000x+1400x^{2}=0$$

Factor out x.

$$x\left(3000+1400x\right)=0$$

To find equation solutions, solve x=0 and 3000+1400x=0.

$$x=0 x=-\frac{15}{7}$$

Variable x cannot be equal to 0.

$$x=-\frac{15}{7}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3000+\frac{5}{6}x\times \frac{3000}{x}x=1100x$$

Multiply x and x to get x^{2}.

$$3000+\frac{5}{6}x^{2}\times \frac{3000}{x}=1100x$$

Multiply \frac{5}{6} times \frac{3000}{x} by multiplying numerator times numerator and denominator times denominator.

$$3000+\frac{5\times 3000}{6x}x^{2}=1100x$$

Cancel out 6 in both numerator and denominator.

$$3000+\frac{5\times 500}{x}x^{2}=1100x$$

Multiply 5 and 500 to get 2500.

$$3000+\frac{2500}{x}x^{2}=1100x$$

Express \frac{2500}{x}x^{2} as a single fraction.

$$3000+\frac{2500x^{2}}{x}=1100x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3000 times \frac{x}{x}.

$$\frac{3000x}{x}+\frac{2500x^{2}}{x}=1100x$$

Since \frac{3000x}{x} and \frac{2500x^{2}}{x} have the same denominator, add them by adding their numerators.

$$\frac{3000x+2500x^{2}}{x}=1100x$$

Subtract 1100x from both sides.

$$\frac{3000x+2500x^{2}}{x}-1100x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -1100x times \frac{x}{x}.

$$\frac{3000x+2500x^{2}}{x}+\frac{-1100xx}{x}=0$$

Since \frac{3000x+2500x^{2}}{x} and \frac{-1100xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{3000x+2500x^{2}-1100xx}{x}=0$$

Do the multiplications in 3000x+2500x^{2}-1100xx.

$$\frac{3000x+2500x^{2}-1100x^{2}}{x}=0$$

Combine like terms in 3000x+2500x^{2}-1100x^{2}.

$$\frac{3000x+1400x^{2}}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3000x+1400x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$1400x^{2}+3000x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1400 for a, 3000 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3000±\sqrt{3000^{2}}}{2\times 1400}$$

Take the square root of 3000^{2}.

$$x=\frac{-3000±3000}{2\times 1400}$$

Multiply 2 times 1400.

$$x=\frac{-3000±3000}{2800}$$

Now solve the equation x=\frac{-3000±3000}{2800} when ± is plus. Add -3000 to 3000.

$$x=\frac{0}{2800}$$

Divide 0 by 2800.

$$x=0$$

Now solve the equation x=\frac{-3000±3000}{2800} when ± is minus. Subtract 3000 from -3000.

$$x=-\frac{6000}{2800}$$

Reduce the fraction \frac{-6000}{2800} to lowest terms by extracting and canceling out 400.

$$x=-\frac{15}{7}$$

The equation is now solved.

$$x=0 x=-\frac{15}{7}$$

Variable x cannot be equal to 0.

$$x=-\frac{15}{7}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3000+\frac{5}{6}x\times \frac{3000}{x}x=1100x$$

Multiply x and x to get x^{2}.

$$3000+\frac{5}{6}x^{2}\times \frac{3000}{x}=1100x$$

Multiply \frac{5}{6} times \frac{3000}{x} by multiplying numerator times numerator and denominator times denominator.

$$3000+\frac{5\times 3000}{6x}x^{2}=1100x$$

Cancel out 6 in both numerator and denominator.

$$3000+\frac{5\times 500}{x}x^{2}=1100x$$

Multiply 5 and 500 to get 2500.

$$3000+\frac{2500}{x}x^{2}=1100x$$

Express \frac{2500}{x}x^{2} as a single fraction.

$$3000+\frac{2500x^{2}}{x}=1100x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3000 times \frac{x}{x}.

$$\frac{3000x}{x}+\frac{2500x^{2}}{x}=1100x$$

Since \frac{3000x}{x} and \frac{2500x^{2}}{x} have the same denominator, add them by adding their numerators.

$$\frac{3000x+2500x^{2}}{x}=1100x$$

Subtract 1100x from both sides.

$$\frac{3000x+2500x^{2}}{x}-1100x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -1100x times \frac{x}{x}.

$$\frac{3000x+2500x^{2}}{x}+\frac{-1100xx}{x}=0$$

Since \frac{3000x+2500x^{2}}{x} and \frac{-1100xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{3000x+2500x^{2}-1100xx}{x}=0$$

Do the multiplications in 3000x+2500x^{2}-1100xx.

$$\frac{3000x+2500x^{2}-1100x^{2}}{x}=0$$

Combine like terms in 3000x+2500x^{2}-1100x^{2}.

$$\frac{3000x+1400x^{2}}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3000x+1400x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$1400x^{2}+3000x=0$$

Divide both sides by 1400.

$$\frac{1400x^{2}+3000x}{1400}=\frac{0}{1400}$$

Dividing by 1400 undoes the multiplication by 1400.

$$x^{2}+\frac{3000}{1400}x=\frac{0}{1400}$$

Reduce the fraction \frac{3000}{1400} to lowest terms by extracting and canceling out 200.

$$x^{2}+\frac{15}{7}x=\frac{0}{1400}$$

Divide 0 by 1400.

$$x^{2}+\frac{15}{7}x=0$$

Divide \frac{15}{7}, the coefficient of the x term, by 2 to get \frac{15}{14}. Then add the square of \frac{15}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{15}{7}x+\left(\frac{15}{14}\right)^{2}=\left(\frac{15}{14}\right)^{2}$$

Square \frac{15}{14} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{15}{7}x+\frac{225}{196}=\frac{225}{196}$$

Factor x^{2}+\frac{15}{7}x+\frac{225}{196}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{15}{14}\right)^{2}=\frac{225}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{15}{14}\right)^{2}}=\sqrt{\frac{225}{196}}$$

Simplify.

$$x+\frac{15}{14}=\frac{15}{14} x+\frac{15}{14}=-\frac{15}{14}$$

Subtract \frac{15}{14} from both sides of the equation.

$$x=0 x=-\frac{15}{7}$$

Variable x cannot be equal to 0.

$$x=-\frac{15}{7}$$