Solve (0.01-x)(0.001-x)=1.08x_{10}-10

$$( 0.01 - x ) ( 0.001 - x ) = 1.08 x _ { 10 } - 10$$

Solve for x_10

$$x_{10}=\frac{25x^{2}}{27}-\frac{11x}{1080}+\frac{1000001}{108000}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.01-x by 0.001-x and combine like terms.

$$0.00001-0.011x+x^{2}=1.08x_{10}-10$$

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

$$1.08x_{10}-10=0.00001-0.011x+x^{2}$$

Add 10 to both sides.

$$1.08x_{10}=0.00001-0.011x+x^{2}+10$$

Add 0.00001 and 10 to get 10.00001.

$$1.08x_{10}=10.00001-0.011x+x^{2}$$

The equation is in standard form.

$$1.08x_{10}=x^{2}-\frac{11x}{1000}+10.00001$$

Divide both sides of the equation by 1.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{1.08x_{10}}{1.08}=\frac{x^{2}-\frac{11x}{1000}+10.00001}{1.08}$$

Dividing by 1.08 undoes the multiplication by 1.08.

$$x_{10}=\frac{x^{2}-\frac{11x}{1000}+10.00001}{1.08}$$

Divide 10.00001-\frac{11x}{1000}+x^{2} by 1.08 by multiplying 10.00001-\frac{11x}{1000}+x^{2} by the reciprocal of 1.08.

$$x_{10}=\frac{25x^{2}}{27}-\frac{11x}{1080}+\frac{1000001}{108000}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{\frac{108x_{10}}{25}-39.999919}}{2}+0.0055$$

$$x=\frac{\sqrt{\frac{108x_{10}}{25}-39.999919}}{2}+0.0055$$

Solve for x

$$x=\frac{\sqrt{\frac{108x_{10}}{25}-39.999919}}{2}+0.0055$$

$$x=-\frac{\sqrt{\frac{108x_{10}}{25}-39.999919}}{2}+0.0055\text{, }x_{10}\geq \frac{39999919}{4320000}$$