Solve 4000(1+x)(1-x)=3940

$$4000 ( 1 + x ) ( 1 - x ) = 3940$$

Solve for x

$$x=\frac{\sqrt{6}}{20}\approx 0.122474487$$

$$x=-\frac{\sqrt{6}}{20}\approx -0.122474487$$

Steps by Finding Square Root

Use the distributive property to multiply 4000 by 1+x.

$$\left(4000+4000x\right)\left(1-x\right)=3940$$

Use the distributive property to multiply 4000+4000x by 1-x and combine like terms.

$$4000-4000x^{2}=3940$$

Subtract 4000 from both sides.

$$-4000x^{2}=3940-4000$$

Subtract 4000 from 3940 to get -60.

$$-4000x^{2}=-60$$

Divide both sides by -4000.

$$x^{2}=\frac{-60}{-4000}$$

Reduce the fraction \frac{-60}{-4000} to lowest terms by extracting and canceling out -20.

$$x^{2}=\frac{3}{200}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{20} x=-\frac{\sqrt{6}}{20}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4000 by 1+x.

$$\left(4000+4000x\right)\left(1-x\right)=3940$$

Use the distributive property to multiply 4000+4000x by 1-x and combine like terms.

$$4000-4000x^{2}=3940$$

Subtract 3940 from both sides.

$$4000-4000x^{2}-3940=0$$

Subtract 3940 from 4000 to get 60.

$$60-4000x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-4000x^{2}+60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4000 for a, 0 for b, and 60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4000\right)\times 60}}{2\left(-4000\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4000\right)\times 60}}{2\left(-4000\right)}$$

Multiply -4 times -4000.

$$x=\frac{0±\sqrt{16000\times 60}}{2\left(-4000\right)}$$

Multiply 16000 times 60.

$$x=\frac{0±\sqrt{960000}}{2\left(-4000\right)}$$

Take the square root of 960000.

$$x=\frac{0±400\sqrt{6}}{2\left(-4000\right)}$$

Multiply 2 times -4000.

$$x=\frac{0±400\sqrt{6}}{-8000}$$

Now solve the equation x=\frac{0±400\sqrt{6}}{-8000} when ± is plus.

$$x=-\frac{\sqrt{6}}{20}$$

Now solve the equation x=\frac{0±400\sqrt{6}}{-8000} when ± is minus.

$$x=\frac{\sqrt{6}}{20}$$

The equation is now solved.

$$x=-\frac{\sqrt{6}}{20} x=\frac{\sqrt{6}}{20}$$