Solve 2.25*9.8*1000*12*(1+0.576divx)+1000000divx=2000000

$$2.25 \times 9.8 \times 1000 \times 12 \times (1+0.576 \div x)+1000000 \div x=2000000$$

Solve for x

$$x=\frac{720256}{1084625}\approx 0.664059929$$

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.

$$2.25\times 9.8\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 2.25 and 9.8 to get 22.05.

$$22.05\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 22.05 and 1000 to get 22050.

$$22050\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 22050 and 12 to get 264600.

$$264600\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Use the distributive property to multiply 264600 by 1+\frac{0.576}{x}.

$$\left(264600+264600\times \frac{0.576}{x}\right)x+1000000=2000000x$$

Use the distributive property to multiply 264600+264600\times \frac{0.576}{x} by x.

$$264600x+264600\times \frac{0.576}{x}x+1000000=2000000x$$

Subtract 2000000x from both sides.

$$264600x+264600\times \frac{0.576}{x}x+1000000-2000000x=0$$

Combine 264600x and -2000000x to get -1735400x.

$$-1735400x+264600\times \frac{0.576}{x}x+1000000=0$$

Subtract 1000000 from both sides. Anything subtracted from zero gives its negation.

$$-1735400x+264600\times \frac{0.576}{x}x=-1000000$$

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

$$-1735400xx+264600\times 0.576x=-1000000x$$

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

$$-1735400x^{2}+264600\times 0.576x=-1000000x$$

Multiply 264600 and 0.576 to get 152409.6.

$$-1735400x^{2}+152409.6x=-1000000x$$

Add 1000000x to both sides.

$$-1735400x^{2}+152409.6x+1000000x=0$$

Combine 152409.6x and 1000000x to get 1152409.6x.

$$-1735400x^{2}+1152409.6x=0$$

Factor out x.

$$x\left(-1735400x+1152409.6\right)=0$$

To find equation solutions, solve x=0 and -1735400x+1152409.6=0.

$$x=0 x=\frac{720256}{1084625}$$

Variable x cannot be equal to 0.

$$x=\frac{720256}{1084625}$$

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.

$$2.25\times 9.8\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 2.25 and 9.8 to get 22.05.

$$22.05\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 22.05 and 1000 to get 22050.

$$22050\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 22050 and 12 to get 264600.

$$264600\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Use the distributive property to multiply 264600 by 1+\frac{0.576}{x}.

$$\left(264600+264600\times \frac{0.576}{x}\right)x+1000000=2000000x$$

Use the distributive property to multiply 264600+264600\times \frac{0.576}{x} by x.

$$264600x+264600\times \frac{0.576}{x}x+1000000=2000000x$$

Subtract 2000000x from both sides.

$$264600x+264600\times \frac{0.576}{x}x+1000000-2000000x=0$$

Combine 264600x and -2000000x to get -1735400x.

$$-1735400x+264600\times \frac{0.576}{x}x+1000000=0$$

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

$$-1735400xx+264600\times 0.576x+x\times 1000000=0$$

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

$$-1735400x^{2}+264600\times 0.576x+x\times 1000000=0$$

Multiply 264600 and 0.576 to get 152409.6.

$$-1735400x^{2}+152409.6x+x\times 1000000=0$$

Combine 152409.6x and x\times 1000000 to get 1152409.6x.

$$-1735400x^{2}+1152409.6x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1735400 for a, 1152409.6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1152409.6±\sqrt{1152409.6^{2}}}{2\left(-1735400\right)}$$

Take the square root of 1152409.6^{2}.

$$x=\frac{-1152409.6±\frac{5762048}{5}}{2\left(-1735400\right)}$$

Multiply 2 times -1735400.

$$x=\frac{-1152409.6±\frac{5762048}{5}}{-3470800}$$

Now solve the equation x=\frac{-1152409.6±\frac{5762048}{5}}{-3470800} when ± is plus. Add -1152409.6 to \frac{5762048}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{-3470800}$$

Divide 0 by -3470800.

$$x=0$$

Now solve the equation x=\frac{-1152409.6±\frac{5762048}{5}}{-3470800} when ± is minus. Subtract \frac{5762048}{5} from -1152409.6 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{11524096}{5}}{-3470800}$$

Divide -\frac{11524096}{5} by -3470800.

$$x=\frac{720256}{1084625}$$

The equation is now solved.

$$x=0 x=\frac{720256}{1084625}$$

Variable x cannot be equal to 0.

$$x=\frac{720256}{1084625}$$

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.

$$2.25\times 9.8\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 2.25 and 9.8 to get 22.05.

$$22.05\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 22.05 and 1000 to get 22050.

$$22050\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Multiply 22050 and 12 to get 264600.

$$264600\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Use the distributive property to multiply 264600 by 1+\frac{0.576}{x}.

$$\left(264600+264600\times \frac{0.576}{x}\right)x+1000000=2000000x$$

Use the distributive property to multiply 264600+264600\times \frac{0.576}{x} by x.

$$264600x+264600\times \frac{0.576}{x}x+1000000=2000000x$$

Subtract 2000000x from both sides.

$$264600x+264600\times \frac{0.576}{x}x+1000000-2000000x=0$$

Combine 264600x and -2000000x to get -1735400x.

$$-1735400x+264600\times \frac{0.576}{x}x+1000000=0$$

Subtract 1000000 from both sides. Anything subtracted from zero gives its negation.

$$-1735400x+264600\times \frac{0.576}{x}x=-1000000$$

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

$$-1735400xx+264600\times 0.576x=-1000000x$$

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

$$-1735400x^{2}+264600\times 0.576x=-1000000x$$

Multiply 264600 and 0.576 to get 152409.6.

$$-1735400x^{2}+152409.6x=-1000000x$$

Add 1000000x to both sides.

$$-1735400x^{2}+152409.6x+1000000x=0$$

Combine 152409.6x and 1000000x to get 1152409.6x.

$$-1735400x^{2}+1152409.6x=0$$

Divide both sides by -1735400.

$$\frac{-1735400x^{2}+1152409.6x}{-1735400}=\frac{0}{-1735400}$$

Dividing by -1735400 undoes the multiplication by -1735400.

$$x^{2}+\frac{1152409.6}{-1735400}x=\frac{0}{-1735400}$$

Divide 1152409.6 by -1735400.

$$x^{2}-\frac{720256}{1084625}x=\frac{0}{-1735400}$$

Divide 0 by -1735400.

$$x^{2}-\frac{720256}{1084625}x=0$$

Divide -\frac{720256}{1084625}, the coefficient of the x term, by 2 to get -\frac{360128}{1084625}. Then add the square of -\frac{360128}{1084625} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{720256}{1084625}x+\left(-\frac{360128}{1084625}\right)^{2}=\left(-\frac{360128}{1084625}\right)^{2}$$

Square -\frac{360128}{1084625} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{720256}{1084625}x+\frac{129692176384}{1176411390625}=\frac{129692176384}{1176411390625}$$

Factor x^{2}-\frac{720256}{1084625}x+\frac{129692176384}{1176411390625}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{360128}{1084625}\right)^{2}=\frac{129692176384}{1176411390625}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{360128}{1084625}\right)^{2}}=\sqrt{\frac{129692176384}{1176411390625}}$$

Simplify.

$$x-\frac{360128}{1084625}=\frac{360128}{1084625} x-\frac{360128}{1084625}=-\frac{360128}{1084625}$$

Add \frac{360128}{1084625} to both sides of the equation.

$$x=\frac{720256}{1084625} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{720256}{1084625}$$