Solve (2000-2000x)*5(1-2x)*0.13=936

$$(2000-2000x) \times 5(1-2x) \times 0.13=936$$

Solve for x

$$x=0.1$$

$$x=1.4$$

Steps Using the Quadratic Formula

Multiply 5 and 0.13 to get 0.65.

$$\left(2000-2000x\right)\times 0.65\left(1-2x\right)=936$$

Use the distributive property to multiply 2000-2000x by 0.65.

$$\left(1300-1300x\right)\left(1-2x\right)=936$$

Use the distributive property to multiply 1300-1300x by 1-2x and combine like terms.

$$1300-3900x+2600x^{2}=936$$

Subtract 936 from both sides.

$$1300-3900x+2600x^{2}-936=0$$

Subtract 936 from 1300 to get 364.

$$364-3900x+2600x^{2}=0$$

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.

$$2600x^{2}-3900x+364=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2600 for a, -3900 for b, and 364 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3900\right)±\sqrt{\left(-3900\right)^{2}-4\times 2600\times 364}}{2\times 2600}$$

Square -3900.

$$x=\frac{-\left(-3900\right)±\sqrt{15210000-4\times 2600\times 364}}{2\times 2600}$$

Multiply -4 times 2600.

$$x=\frac{-\left(-3900\right)±\sqrt{15210000-10400\times 364}}{2\times 2600}$$

Multiply -10400 times 364.

$$x=\frac{-\left(-3900\right)±\sqrt{15210000-3785600}}{2\times 2600}$$

Add 15210000 to -3785600.

$$x=\frac{-\left(-3900\right)±\sqrt{11424400}}{2\times 2600}$$

Take the square root of 11424400.

$$x=\frac{-\left(-3900\right)±3380}{2\times 2600}$$

The opposite of -3900 is 3900.

$$x=\frac{3900±3380}{2\times 2600}$$

Multiply 2 times 2600.

$$x=\frac{3900±3380}{5200}$$

Now solve the equation x=\frac{3900±3380}{5200} when ± is plus. Add 3900 to 3380.

$$x=\frac{7280}{5200}$$

Reduce the fraction \frac{7280}{5200} to lowest terms by extracting and canceling out 1040.

$$x=\frac{7}{5}$$

Now solve the equation x=\frac{3900±3380}{5200} when ± is minus. Subtract 3380 from 3900.

$$x=\frac{520}{5200}$$

Reduce the fraction \frac{520}{5200} to lowest terms by extracting and canceling out 520.

$$x=\frac{1}{10}$$

The equation is now solved.

$$x=\frac{7}{5} x=\frac{1}{10}$$

Steps for Completing the Square

Multiply 5 and 0.13 to get 0.65.

$$\left(2000-2000x\right)\times 0.65\left(1-2x\right)=936$$

Use the distributive property to multiply 2000-2000x by 0.65.

$$\left(1300-1300x\right)\left(1-2x\right)=936$$

Use the distributive property to multiply 1300-1300x by 1-2x and combine like terms.

$$1300-3900x+2600x^{2}=936$$

Subtract 1300 from both sides.

$$-3900x+2600x^{2}=936-1300$$

Subtract 1300 from 936 to get -364.

$$-3900x+2600x^{2}=-364$$

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.

$$2600x^{2}-3900x=-364$$

Divide both sides by 2600.

$$\frac{2600x^{2}-3900x}{2600}=-\frac{364}{2600}$$

Dividing by 2600 undoes the multiplication by 2600.

$$x^{2}+\left(-\frac{3900}{2600}\right)x=-\frac{364}{2600}$$

Reduce the fraction \frac{-3900}{2600} to lowest terms by extracting and canceling out 1300.

$$x^{2}-\frac{3}{2}x=-\frac{364}{2600}$$

Reduce the fraction \frac{-364}{2600} to lowest terms by extracting and canceling out 52.

$$x^{2}-\frac{3}{2}x=-\frac{7}{50}$$

Divide -\frac{3}{2}, the coefficient of the x term, by 2 to get -\frac{3}{4}. Then add the square of -\frac{3}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{3}{2}x+\left(-\frac{3}{4}\right)^{2}=-\frac{7}{50}+\left(-\frac{3}{4}\right)^{2}$$

Square -\frac{3}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=-\frac{7}{50}+\frac{9}{16}$$

Add -\frac{7}{50} to \frac{9}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{169}{400}$$

Factor x^{2}-\frac{3}{2}x+\frac{9}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3}{4}\right)^{2}=\frac{169}{400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{\frac{169}{400}}$$

Simplify.

$$x-\frac{3}{4}=\frac{13}{20} x-\frac{3}{4}=-\frac{13}{20}$$

Add \frac{3}{4} to both sides of the equation.

$$x=\frac{7}{5} x=\frac{1}{10}$$