Solve 4.04=470divx/470+(470divx)*10

$$4.04= \frac{ 470 \div x }{ 470+(470 \div x) } \times 10$$

Solve for x

$$x = \frac{149}{101} = 1\frac{48}{101} \approx 1.475247525$$

Steps Using Factoring

Divide both sides by 10.

$$\frac{4.04}{10}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Expand \frac{4.04}{10} by multiplying both numerator and the denominator by 100.

$$\frac{404}{1000}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Reduce the fraction \frac{404}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{101}{250}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Express \frac{\frac{470}{x}}{470+\frac{470}{x}} as a single fraction.

$$\frac{101}{250}=\frac{470}{x\left(470+\frac{470}{x}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 470 times \frac{x}{x}.

$$\frac{101}{250}=\frac{470}{x\left(\frac{470x}{x}+\frac{470}{x}\right)}$$

Since \frac{470x}{x} and \frac{470}{x} have the same denominator, add them by adding their numerators.

$$\frac{101}{250}=\frac{470}{x\times \frac{470x+470}{x}}$$

Express x\times \frac{470x+470}{x} as a single fraction.

$$\frac{101}{250}=\frac{470}{\frac{x\left(470x+470\right)}{x}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 470 by \frac{x\left(470x+470\right)}{x} by multiplying 470 by the reciprocal of \frac{x\left(470x+470\right)}{x}.

$$\frac{101}{250}=\frac{470x}{x\left(470x+470\right)}$$

Factor the expressions that are not already factored in \frac{470x}{x\left(470x+470\right)}.

$$\frac{101}{250}=\frac{470x}{470x\left(x+1\right)}$$

Cancel out 470 in both numerator and denominator.

$$\frac{101}{250}=\frac{x}{x\left(x+1\right)}$$

Use the distributive property to multiply x by x+1.

$$\frac{101}{250}=\frac{x}{x^{2}+x}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x}{x^{2}+x}=\frac{101}{250}$$

Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by 250x\left(x+1\right), the least common multiple of x^{2}+x,250.

$$250x=101x\left(x+1\right)$$

Use the distributive property to multiply 101x by x+1.

$$250x=101x^{2}+101x$$

Subtract 101x^{2} from both sides.

$$250x-101x^{2}=101x$$

Subtract 101x from both sides.

$$250x-101x^{2}-101x=0$$

Combine 250x and -101x to get 149x.

$$149x-101x^{2}=0$$

Factor out x.

$$x\left(149-101x\right)=0$$

To find equation solutions, solve x=0 and 149-101x=0.

$$x=0 x=\frac{149}{101}$$

Variable x cannot be equal to 0.

$$x=\frac{149}{101}$$

Steps Using the Quadratic Formula

Divide both sides by 10.

$$\frac{4.04}{10}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Expand \frac{4.04}{10} by multiplying both numerator and the denominator by 100.

$$\frac{404}{1000}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Reduce the fraction \frac{404}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{101}{250}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Express \frac{\frac{470}{x}}{470+\frac{470}{x}} as a single fraction.

$$\frac{101}{250}=\frac{470}{x\left(470+\frac{470}{x}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 470 times \frac{x}{x}.

$$\frac{101}{250}=\frac{470}{x\left(\frac{470x}{x}+\frac{470}{x}\right)}$$

Since \frac{470x}{x} and \frac{470}{x} have the same denominator, add them by adding their numerators.

$$\frac{101}{250}=\frac{470}{x\times \frac{470x+470}{x}}$$

Express x\times \frac{470x+470}{x} as a single fraction.

$$\frac{101}{250}=\frac{470}{\frac{x\left(470x+470\right)}{x}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 470 by \frac{x\left(470x+470\right)}{x} by multiplying 470 by the reciprocal of \frac{x\left(470x+470\right)}{x}.

$$\frac{101}{250}=\frac{470x}{x\left(470x+470\right)}$$

Factor the expressions that are not already factored in \frac{470x}{x\left(470x+470\right)}.

$$\frac{101}{250}=\frac{470x}{470x\left(x+1\right)}$$

Cancel out 470 in both numerator and denominator.

$$\frac{101}{250}=\frac{x}{x\left(x+1\right)}$$

Use the distributive property to multiply x by x+1.

$$\frac{101}{250}=\frac{x}{x^{2}+x}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x}{x^{2}+x}=\frac{101}{250}$$

Subtract \frac{101}{250} from both sides.

$$\frac{x}{x^{2}+x}-\frac{101}{250}=0$$

Factor x^{2}+x.

$$\frac{x}{x\left(x+1\right)}-\frac{101}{250}=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x+1\right) and 250 is 250x\left(x+1\right). Multiply \frac{x}{x\left(x+1\right)} times \frac{250}{250}. Multiply \frac{101}{250} times \frac{x\left(x+1\right)}{x\left(x+1\right)}.

$$\frac{250x}{250x\left(x+1\right)}-\frac{101x\left(x+1\right)}{250x\left(x+1\right)}=0$$

Since \frac{250x}{250x\left(x+1\right)} and \frac{101x\left(x+1\right)}{250x\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{250x-101x\left(x+1\right)}{250x\left(x+1\right)}=0$$

Do the multiplications in 250x-101x\left(x+1\right).

$$\frac{250x-101x^{2}-101x}{250x\left(x+1\right)}=0$$

Combine like terms in 250x-101x^{2}-101x.

$$\frac{149x-101x^{2}}{250x\left(x+1\right)}=0$$

Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by 250x\left(x+1\right).

$$149x-101x^{2}=0$$

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.

$$-101x^{2}+149x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -101 for a, 149 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-149±\sqrt{149^{2}}}{2\left(-101\right)}$$

Take the square root of 149^{2}.

$$x=\frac{-149±149}{2\left(-101\right)}$$

Multiply 2 times -101.

$$x=\frac{-149±149}{-202}$$

Now solve the equation x=\frac{-149±149}{-202} when ± is plus. Add -149 to 149.

$$x=\frac{0}{-202}$$

Divide 0 by -202.

$$x=0$$

Now solve the equation x=\frac{-149±149}{-202} when ± is minus. Subtract 149 from -149.

$$x=-\frac{298}{-202}$$

Reduce the fraction \frac{-298}{-202} to lowest terms by extracting and canceling out 2.

$$x=\frac{149}{101}$$

The equation is now solved.

$$x=0 x=\frac{149}{101}$$

Variable x cannot be equal to 0.

$$x=\frac{149}{101}$$

Steps for Completing the Square

Divide both sides by 10.

$$\frac{4.04}{10}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Expand \frac{4.04}{10} by multiplying both numerator and the denominator by 100.

$$\frac{404}{1000}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Reduce the fraction \frac{404}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{101}{250}=\frac{\frac{470}{x}}{470+\frac{470}{x}}$$

Express \frac{\frac{470}{x}}{470+\frac{470}{x}} as a single fraction.

$$\frac{101}{250}=\frac{470}{x\left(470+\frac{470}{x}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 470 times \frac{x}{x}.

$$\frac{101}{250}=\frac{470}{x\left(\frac{470x}{x}+\frac{470}{x}\right)}$$

Since \frac{470x}{x} and \frac{470}{x} have the same denominator, add them by adding their numerators.

$$\frac{101}{250}=\frac{470}{x\times \frac{470x+470}{x}}$$

Express x\times \frac{470x+470}{x} as a single fraction.

$$\frac{101}{250}=\frac{470}{\frac{x\left(470x+470\right)}{x}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 470 by \frac{x\left(470x+470\right)}{x} by multiplying 470 by the reciprocal of \frac{x\left(470x+470\right)}{x}.

$$\frac{101}{250}=\frac{470x}{x\left(470x+470\right)}$$

Factor the expressions that are not already factored in \frac{470x}{x\left(470x+470\right)}.

$$\frac{101}{250}=\frac{470x}{470x\left(x+1\right)}$$

Cancel out 470 in both numerator and denominator.

$$\frac{101}{250}=\frac{x}{x\left(x+1\right)}$$

Use the distributive property to multiply x by x+1.

$$\frac{101}{250}=\frac{x}{x^{2}+x}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x}{x^{2}+x}=\frac{101}{250}$$

Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by 250x\left(x+1\right), the least common multiple of x^{2}+x,250.

$$250x=101x\left(x+1\right)$$

Use the distributive property to multiply 101x by x+1.

$$250x=101x^{2}+101x$$

Subtract 101x^{2} from both sides.

$$250x-101x^{2}=101x$$

Subtract 101x from both sides.

$$250x-101x^{2}-101x=0$$

Combine 250x and -101x to get 149x.

$$149x-101x^{2}=0$$

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.

$$-101x^{2}+149x=0$$

Divide both sides by -101.

$$\frac{-101x^{2}+149x}{-101}=\frac{0}{-101}$$

Dividing by -101 undoes the multiplication by -101.

$$x^{2}+\frac{149}{-101}x=\frac{0}{-101}$$

Divide 149 by -101.

$$x^{2}-\frac{149}{101}x=\frac{0}{-101}$$

Divide 0 by -101.

$$x^{2}-\frac{149}{101}x=0$$

Divide -\frac{149}{101}, the coefficient of the x term, by 2 to get -\frac{149}{202}. Then add the square of -\frac{149}{202} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{149}{101}x+\left(-\frac{149}{202}\right)^{2}=\left(-\frac{149}{202}\right)^{2}$$

Square -\frac{149}{202} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{149}{101}x+\frac{22201}{40804}=\frac{22201}{40804}$$

Factor x^{2}-\frac{149}{101}x+\frac{22201}{40804}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{149}{202}\right)^{2}=\frac{22201}{40804}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{149}{202}\right)^{2}}=\sqrt{\frac{22201}{40804}}$$

Simplify.

$$x-\frac{149}{202}=\frac{149}{202} x-\frac{149}{202}=-\frac{149}{202}$$

Add \frac{149}{202} to both sides of the equation.

$$x=\frac{149}{101} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{149}{101}$$