Solve 225*98*1000*12*(1+0576divx)+1000000divx=2000000

$$225 \times 98 \times 1000 \times 12 \times (1+0576 \div x)+1000000 \div x=2000000$$

Solve for x

$$x=-\frac{5}{1313}\approx -0.003808073$$

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.

$$225\times 98\times 1000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 225 and 98 to get 22050.

$$22050\times 1000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 22050 and 1000 to get 22050000.

$$22050000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 22050000 and 12 to get 264600000.

$$264600000\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 0 and 576 to get 0.

$$264600000\left(1+\frac{0}{x}\right)x+1000000=2000000x$$

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

$$264600000\left(\frac{x}{x}+\frac{0}{x}\right)x+1000000=2000000x$$

Since \frac{x}{x} and \frac{0}{x} have the same denominator, add them by adding their numerators.

$$264600000\times \frac{x+0}{x}x+1000000=2000000x$$

Combine like terms in x+0.

$$264600000\times \frac{x}{x}x+1000000=2000000x$$

Express 264600000\times \frac{x}{x} as a single fraction.

$$\frac{264600000x}{x}x+1000000=2000000x$$

Express \frac{264600000x}{x}x as a single fraction.

$$\frac{264600000xx}{x}+1000000=2000000x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1000000 times \frac{x}{x}.

$$\frac{264600000xx}{x}+\frac{1000000x}{x}=2000000x$$

Since \frac{264600000xx}{x} and \frac{1000000x}{x} have the same denominator, add them by adding their numerators.

$$\frac{264600000xx+1000000x}{x}=2000000x$$

Do the multiplications in 264600000xx+1000000x.

$$\frac{264600000x^{2}+1000000x}{x}=2000000x$$

Subtract 2000000x from both sides.

$$\frac{264600000x^{2}+1000000x}{x}-2000000x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2000000x times \frac{x}{x}.

$$\frac{264600000x^{2}+1000000x}{x}+\frac{-2000000xx}{x}=0$$

Since \frac{264600000x^{2}+1000000x}{x} and \frac{-2000000xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{264600000x^{2}+1000000x-2000000xx}{x}=0$$

Do the multiplications in 264600000x^{2}+1000000x-2000000xx.

$$\frac{264600000x^{2}+1000000x-2000000x^{2}}{x}=0$$

Combine like terms in 264600000x^{2}+1000000x-2000000x^{2}.

$$\frac{262600000x^{2}+1000000x}{x}=0$$

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

$$262600000x^{2}+1000000x=0$$

Factor out x.

$$x\left(262600000x+1000000\right)=0$$

To find equation solutions, solve x=0 and 262600000x+1000000=0.

$$x=0 x=-\frac{5}{1313}$$

Variable x cannot be equal to 0.

$$x=-\frac{5}{1313}$$

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.

$$225\times 98\times 1000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 225 and 98 to get 22050.

$$22050\times 1000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 22050 and 1000 to get 22050000.

$$22050000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 22050000 and 12 to get 264600000.

$$264600000\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 0 and 576 to get 0.

$$264600000\left(1+\frac{0}{x}\right)x+1000000=2000000x$$

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

$$264600000\left(\frac{x}{x}+\frac{0}{x}\right)x+1000000=2000000x$$

Since \frac{x}{x} and \frac{0}{x} have the same denominator, add them by adding their numerators.

$$264600000\times \frac{x+0}{x}x+1000000=2000000x$$

Combine like terms in x+0.

$$264600000\times \frac{x}{x}x+1000000=2000000x$$

Express 264600000\times \frac{x}{x} as a single fraction.

$$\frac{264600000x}{x}x+1000000=2000000x$$

Express \frac{264600000x}{x}x as a single fraction.

$$\frac{264600000xx}{x}+1000000=2000000x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1000000 times \frac{x}{x}.

$$\frac{264600000xx}{x}+\frac{1000000x}{x}=2000000x$$

Since \frac{264600000xx}{x} and \frac{1000000x}{x} have the same denominator, add them by adding their numerators.

$$\frac{264600000xx+1000000x}{x}=2000000x$$

Do the multiplications in 264600000xx+1000000x.

$$\frac{264600000x^{2}+1000000x}{x}=2000000x$$

Subtract 2000000x from both sides.

$$\frac{264600000x^{2}+1000000x}{x}-2000000x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2000000x times \frac{x}{x}.

$$\frac{264600000x^{2}+1000000x}{x}+\frac{-2000000xx}{x}=0$$

Since \frac{264600000x^{2}+1000000x}{x} and \frac{-2000000xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{264600000x^{2}+1000000x-2000000xx}{x}=0$$

Do the multiplications in 264600000x^{2}+1000000x-2000000xx.

$$\frac{264600000x^{2}+1000000x-2000000x^{2}}{x}=0$$

Combine like terms in 264600000x^{2}+1000000x-2000000x^{2}.

$$\frac{262600000x^{2}+1000000x}{x}=0$$

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

$$262600000x^{2}+1000000x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 262600000 for a, 1000000 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1000000±\sqrt{1000000^{2}}}{2\times 262600000}$$

Take the square root of 1000000^{2}.

$$x=\frac{-1000000±1000000}{2\times 262600000}$$

Multiply 2 times 262600000.

$$x=\frac{-1000000±1000000}{525200000}$$

Now solve the equation x=\frac{-1000000±1000000}{525200000} when ± is plus. Add -1000000 to 1000000.

$$x=\frac{0}{525200000}$$

Divide 0 by 525200000.

$$x=0$$

Now solve the equation x=\frac{-1000000±1000000}{525200000} when ± is minus. Subtract 1000000 from -1000000.

$$x=-\frac{2000000}{525200000}$$

Reduce the fraction \frac{-2000000}{525200000} to lowest terms by extracting and canceling out 400000.

$$x=-\frac{5}{1313}$$

The equation is now solved.

$$x=0 x=-\frac{5}{1313}$$

Variable x cannot be equal to 0.

$$x=-\frac{5}{1313}$$

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.

$$225\times 98\times 1000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 225 and 98 to get 22050.

$$22050\times 1000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 22050 and 1000 to get 22050000.

$$22050000\times 12\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 22050000 and 12 to get 264600000.

$$264600000\left(1+\frac{0\times 576}{x}\right)x+1000000=2000000x$$

Multiply 0 and 576 to get 0.

$$264600000\left(1+\frac{0}{x}\right)x+1000000=2000000x$$

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

$$264600000\left(\frac{x}{x}+\frac{0}{x}\right)x+1000000=2000000x$$

Since \frac{x}{x} and \frac{0}{x} have the same denominator, add them by adding their numerators.

$$264600000\times \frac{x+0}{x}x+1000000=2000000x$$

Combine like terms in x+0.

$$264600000\times \frac{x}{x}x+1000000=2000000x$$

Express 264600000\times \frac{x}{x} as a single fraction.

$$\frac{264600000x}{x}x+1000000=2000000x$$

Express \frac{264600000x}{x}x as a single fraction.

$$\frac{264600000xx}{x}+1000000=2000000x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1000000 times \frac{x}{x}.

$$\frac{264600000xx}{x}+\frac{1000000x}{x}=2000000x$$

Since \frac{264600000xx}{x} and \frac{1000000x}{x} have the same denominator, add them by adding their numerators.

$$\frac{264600000xx+1000000x}{x}=2000000x$$

Do the multiplications in 264600000xx+1000000x.

$$\frac{264600000x^{2}+1000000x}{x}=2000000x$$

Subtract 2000000x from both sides.

$$\frac{264600000x^{2}+1000000x}{x}-2000000x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2000000x times \frac{x}{x}.

$$\frac{264600000x^{2}+1000000x}{x}+\frac{-2000000xx}{x}=0$$

Since \frac{264600000x^{2}+1000000x}{x} and \frac{-2000000xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{264600000x^{2}+1000000x-2000000xx}{x}=0$$

Do the multiplications in 264600000x^{2}+1000000x-2000000xx.

$$\frac{264600000x^{2}+1000000x-2000000x^{2}}{x}=0$$

Combine like terms in 264600000x^{2}+1000000x-2000000x^{2}.

$$\frac{262600000x^{2}+1000000x}{x}=0$$

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

$$262600000x^{2}+1000000x=0$$

Divide both sides by 262600000.

$$\frac{262600000x^{2}+1000000x}{262600000}=\frac{0}{262600000}$$

Dividing by 262600000 undoes the multiplication by 262600000.

$$x^{2}+\frac{1000000}{262600000}x=\frac{0}{262600000}$$

Reduce the fraction \frac{1000000}{262600000} to lowest terms by extracting and canceling out 200000.

$$x^{2}+\frac{5}{1313}x=\frac{0}{262600000}$$

Divide 0 by 262600000.

$$x^{2}+\frac{5}{1313}x=0$$

Divide \frac{5}{1313}, the coefficient of the x term, by 2 to get \frac{5}{2626}. Then add the square of \frac{5}{2626} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{5}{1313}x+\left(\frac{5}{2626}\right)^{2}=\left(\frac{5}{2626}\right)^{2}$$

Square \frac{5}{2626} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{5}{1313}x+\frac{25}{6895876}=\frac{25}{6895876}$$

Factor x^{2}+\frac{5}{1313}x+\frac{25}{6895876}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{2626}\right)^{2}=\frac{25}{6895876}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{2626}\right)^{2}}=\sqrt{\frac{25}{6895876}}$$

Simplify.

$$x+\frac{5}{2626}=\frac{5}{2626} x+\frac{5}{2626}=-\frac{5}{2626}$$

Subtract \frac{5}{2626} from both sides of the equation.

$$x=0 x=-\frac{5}{1313}$$

Variable x cannot be equal to 0.

$$x=-\frac{5}{1313}$$