Solve 0.6-x+1/x*10%*40%-1%/x=0.4

$$0.6 - \frac { x + 1 } { x } \times 10 \% \times 40 \% - \frac { 1 \% } { x } = 0.4$$

Solve for x

$$x=0.3125$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100x, the least common multiple of x,100.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{10}{100}\times \frac{40}{100}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{10}\times \frac{40}{100}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{10}\times \frac{2}{5}\right)-100\times \frac{1}{100}=40x$$

Multiply \frac{1}{10} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1\times 2}{10\times 5}\right)-100\times \frac{1}{100}=40x$$

Do the multiplications in the fraction \frac{1\times 2}{10\times 5}.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{2}{50}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{2}{50} to lowest terms by extracting and canceling out 2.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{25}\right)-100\times \frac{1}{100}=40x$$

Multiply \frac{x+1}{x} times \frac{1}{25} by multiplying numerator times numerator and denominator times denominator.

$$100x\left(0.6-\frac{x+1}{x\times 25}\right)-100\times \frac{1}{100}=40x$$

Use the distributive property to multiply 100x by 0.6-\frac{x+1}{x\times 25}.

$$60x+100x\left(-\frac{x+1}{x\times 25}\right)-100\times \frac{1}{100}=40x$$

Express 100\left(-\frac{x+1}{x\times 25}\right) as a single fraction.

$$60x+\frac{-100\left(x+1\right)}{x\times 25}x-100\times \frac{1}{100}=40x$$

Cancel out 25 in both numerator and denominator.

$$60x+\frac{-4\left(x+1\right)}{x}x-100\times \frac{1}{100}=40x$$

Express \frac{-4\left(x+1\right)}{x}x as a single fraction.

$$60x+\frac{-4\left(x+1\right)x}{x}-100\times \frac{1}{100}=40x$$

Multiply -100 times \frac{1}{100}.

$$60x+\frac{-4\left(x+1\right)x}{x}-1=40x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 60x-1 times \frac{x}{x}.

$$\frac{\left(60x-1\right)x}{x}+\frac{-4\left(x+1\right)x}{x}=40x$$

Since \frac{\left(60x-1\right)x}{x} and \frac{-4\left(x+1\right)x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\left(60x-1\right)x-4\left(x+1\right)x}{x}=40x$$

Do the multiplications in \left(60x-1\right)x-4\left(x+1\right)x.

$$\frac{60x^{2}-x-4x^{2}-4x}{x}=40x$$

Combine like terms in 60x^{2}-x-4x^{2}-4x.

$$\frac{56x^{2}-5x}{x}=40x$$

Subtract 40x from both sides.

$$\frac{56x^{2}-5x}{x}-40x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -40x times \frac{x}{x}.

$$\frac{56x^{2}-5x}{x}+\frac{-40xx}{x}=0$$

Since \frac{56x^{2}-5x}{x} and \frac{-40xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{56x^{2}-5x-40xx}{x}=0$$

Do the multiplications in 56x^{2}-5x-40xx.

$$\frac{56x^{2}-5x-40x^{2}}{x}=0$$

Combine like terms in 56x^{2}-5x-40x^{2}.

$$\frac{16x^{2}-5x}{x}=0$$

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

$$16x^{2}-5x=0$$

Factor out x.

$$x\left(16x-5\right)=0$$

To find equation solutions, solve x=0 and 16x-5=0.

$$x=0 x=\frac{5}{16}$$

Variable x cannot be equal to 0.

$$x=\frac{5}{16}$$

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 100x, the least common multiple of x,100.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{10}{100}\times \frac{40}{100}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{10}\times \frac{40}{100}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{10}\times \frac{2}{5}\right)-100\times \frac{1}{100}=40x$$

Multiply \frac{1}{10} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1\times 2}{10\times 5}\right)-100\times \frac{1}{100}=40x$$

Do the multiplications in the fraction \frac{1\times 2}{10\times 5}.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{2}{50}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{2}{50} to lowest terms by extracting and canceling out 2.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{25}\right)-100\times \frac{1}{100}=40x$$

Multiply \frac{x+1}{x} times \frac{1}{25} by multiplying numerator times numerator and denominator times denominator.

$$100x\left(0.6-\frac{x+1}{x\times 25}\right)-100\times \frac{1}{100}=40x$$

Use the distributive property to multiply 100x by 0.6-\frac{x+1}{x\times 25}.

$$60x+100x\left(-\frac{x+1}{x\times 25}\right)-100\times \frac{1}{100}=40x$$

Express 100\left(-\frac{x+1}{x\times 25}\right) as a single fraction.

$$60x+\frac{-100\left(x+1\right)}{x\times 25}x-100\times \frac{1}{100}=40x$$

Cancel out 25 in both numerator and denominator.

$$60x+\frac{-4\left(x+1\right)}{x}x-100\times \frac{1}{100}=40x$$

Express \frac{-4\left(x+1\right)}{x}x as a single fraction.

$$60x+\frac{-4\left(x+1\right)x}{x}-100\times \frac{1}{100}=40x$$

Multiply -100 times \frac{1}{100}.

$$60x+\frac{-4\left(x+1\right)x}{x}-1=40x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 60x-1 times \frac{x}{x}.

$$\frac{\left(60x-1\right)x}{x}+\frac{-4\left(x+1\right)x}{x}=40x$$

Since \frac{\left(60x-1\right)x}{x} and \frac{-4\left(x+1\right)x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\left(60x-1\right)x-4\left(x+1\right)x}{x}=40x$$

Do the multiplications in \left(60x-1\right)x-4\left(x+1\right)x.

$$\frac{60x^{2}-x-4x^{2}-4x}{x}=40x$$

Combine like terms in 60x^{2}-x-4x^{2}-4x.

$$\frac{56x^{2}-5x}{x}=40x$$

Subtract 40x from both sides.

$$\frac{56x^{2}-5x}{x}-40x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -40x times \frac{x}{x}.

$$\frac{56x^{2}-5x}{x}+\frac{-40xx}{x}=0$$

Since \frac{56x^{2}-5x}{x} and \frac{-40xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{56x^{2}-5x-40xx}{x}=0$$

Do the multiplications in 56x^{2}-5x-40xx.

$$\frac{56x^{2}-5x-40x^{2}}{x}=0$$

Combine like terms in 56x^{2}-5x-40x^{2}.

$$\frac{16x^{2}-5x}{x}=0$$

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

$$16x^{2}-5x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, -5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 16}$$

Take the square root of \left(-5\right)^{2}.

$$x=\frac{-\left(-5\right)±5}{2\times 16}$$

The opposite of -5 is 5.

$$x=\frac{5±5}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{5±5}{32}$$

Now solve the equation x=\frac{5±5}{32} when ± is plus. Add 5 to 5.

$$x=\frac{10}{32}$$

Reduce the fraction \frac{10}{32} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{16}$$

Now solve the equation x=\frac{5±5}{32} when ± is minus. Subtract 5 from 5.

$$x=\frac{0}{32}$$

Divide 0 by 32.

$$x=0$$

The equation is now solved.

$$x=\frac{5}{16} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{5}{16}$$

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 100x, the least common multiple of x,100.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{10}{100}\times \frac{40}{100}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{10}\times \frac{40}{100}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{10}\times \frac{2}{5}\right)-100\times \frac{1}{100}=40x$$

Multiply \frac{1}{10} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1\times 2}{10\times 5}\right)-100\times \frac{1}{100}=40x$$

Do the multiplications in the fraction \frac{1\times 2}{10\times 5}.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{2}{50}\right)-100\times \frac{1}{100}=40x$$

Reduce the fraction \frac{2}{50} to lowest terms by extracting and canceling out 2.

$$100x\left(0.6-\frac{x+1}{x}\times \frac{1}{25}\right)-100\times \frac{1}{100}=40x$$

Multiply \frac{x+1}{x} times \frac{1}{25} by multiplying numerator times numerator and denominator times denominator.

$$100x\left(0.6-\frac{x+1}{x\times 25}\right)-100\times \frac{1}{100}=40x$$

Use the distributive property to multiply 100x by 0.6-\frac{x+1}{x\times 25}.

$$60x+100x\left(-\frac{x+1}{x\times 25}\right)-100\times \frac{1}{100}=40x$$

Express 100\left(-\frac{x+1}{x\times 25}\right) as a single fraction.

$$60x+\frac{-100\left(x+1\right)}{x\times 25}x-100\times \frac{1}{100}=40x$$

Cancel out 25 in both numerator and denominator.

$$60x+\frac{-4\left(x+1\right)}{x}x-100\times \frac{1}{100}=40x$$

Express \frac{-4\left(x+1\right)}{x}x as a single fraction.

$$60x+\frac{-4\left(x+1\right)x}{x}-100\times \frac{1}{100}=40x$$

Multiply -100 times \frac{1}{100}.

$$60x+\frac{-4\left(x+1\right)x}{x}-1=40x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 60x-1 times \frac{x}{x}.

$$\frac{\left(60x-1\right)x}{x}+\frac{-4\left(x+1\right)x}{x}=40x$$

Since \frac{\left(60x-1\right)x}{x} and \frac{-4\left(x+1\right)x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\left(60x-1\right)x-4\left(x+1\right)x}{x}=40x$$

Do the multiplications in \left(60x-1\right)x-4\left(x+1\right)x.

$$\frac{60x^{2}-x-4x^{2}-4x}{x}=40x$$

Combine like terms in 60x^{2}-x-4x^{2}-4x.

$$\frac{56x^{2}-5x}{x}=40x$$

Subtract 40x from both sides.

$$\frac{56x^{2}-5x}{x}-40x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -40x times \frac{x}{x}.

$$\frac{56x^{2}-5x}{x}+\frac{-40xx}{x}=0$$

Since \frac{56x^{2}-5x}{x} and \frac{-40xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{56x^{2}-5x-40xx}{x}=0$$

Do the multiplications in 56x^{2}-5x-40xx.

$$\frac{56x^{2}-5x-40x^{2}}{x}=0$$

Combine like terms in 56x^{2}-5x-40x^{2}.

$$\frac{16x^{2}-5x}{x}=0$$

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

$$16x^{2}-5x=0$$

Divide both sides by 16.

$$\frac{16x^{2}-5x}{16}=\frac{0}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$x^{2}-\frac{5}{16}x=\frac{0}{16}$$

Divide 0 by 16.

$$x^{2}-\frac{5}{16}x=0$$

Divide -\frac{5}{16}, the coefficient of the x term, by 2 to get -\frac{5}{32}. Then add the square of -\frac{5}{32} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{5}{16}x+\left(-\frac{5}{32}\right)^{2}=\left(-\frac{5}{32}\right)^{2}$$

Square -\frac{5}{32} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{5}{16}x+\frac{25}{1024}=\frac{25}{1024}$$

Factor x^{2}-\frac{5}{16}x+\frac{25}{1024}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{5}{32}\right)^{2}=\frac{25}{1024}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{32}\right)^{2}}=\sqrt{\frac{25}{1024}}$$

Simplify.

$$x-\frac{5}{32}=\frac{5}{32} x-\frac{5}{32}=-\frac{5}{32}$$

Add \frac{5}{32} to both sides of the equation.

$$x=\frac{5}{16} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{5}{16}$$