Solve 800*(1+x/10)*(1-x/10)=800-32

$$800 \times ( 1 + \frac { x } { 10 } ) \times ( 1 - \frac { x } { 10 } ) = 800 - 32$$

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

Multiply both sides of the equation by 10.

$$8000\left(1+\frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Use the distributive property to multiply 8000 by 1+\frac{x}{10}.

$$\left(8000+8000\times \frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Cancel out 10, the greatest common factor in 8000 and 10.

$$\left(8000+800x\right)\left(1-\frac{x}{10}\right)=8000-320$$

Apply the distributive property by multiplying each term of 8000+800x by each term of 1-\frac{x}{10}.

$$8000+8000\left(-\frac{x}{10}\right)+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Cancel out 10, the greatest common factor in 8000 and 10.

$$8000-800x+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Combine -800x and 800x to get 0.

$$8000+800x\left(-\frac{x}{10}\right)=8000-320$$

Cancel out 10, the greatest common factor in 800 and 10.

$$8000-80xx=8000-320$$

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

$$8000-80x^{2}=8000-320$$

Subtract 320 from 8000 to get 7680.

$$8000-80x^{2}=7680$$

Subtract 8000 from both sides.

$$-80x^{2}=7680-8000$$

Subtract 8000 from 7680 to get -320.

$$-80x^{2}=-320$$

Divide both sides by -80.

$$x^{2}=\frac{-320}{-80}$$

Divide -320 by -80 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 10.

$$8000\left(1+\frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Use the distributive property to multiply 8000 by 1+\frac{x}{10}.

$$\left(8000+8000\times \frac{x}{10}\right)\left(1-\frac{x}{10}\right)=8000-320$$

Cancel out 10, the greatest common factor in 8000 and 10.

$$\left(8000+800x\right)\left(1-\frac{x}{10}\right)=8000-320$$

Apply the distributive property by multiplying each term of 8000+800x by each term of 1-\frac{x}{10}.

$$8000+8000\left(-\frac{x}{10}\right)+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Cancel out 10, the greatest common factor in 8000 and 10.

$$8000-800x+800x+800x\left(-\frac{x}{10}\right)=8000-320$$

Combine -800x and 800x to get 0.

$$8000+800x\left(-\frac{x}{10}\right)=8000-320$$

Cancel out 10, the greatest common factor in 800 and 10.

$$8000-80xx=8000-320$$

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

$$8000-80x^{2}=8000-320$$

Subtract 320 from 8000 to get 7680.

$$8000-80x^{2}=7680$$

Subtract 7680 from both sides.

$$8000-80x^{2}-7680=0$$

Subtract 7680 from 8000 to get 320.

$$320-80x^{2}=0$$

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.

$$-80x^{2}+320=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -80 for a, 0 for b, and 320 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-80\right)\times 320}}{2\left(-80\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-80\right)\times 320}}{2\left(-80\right)}$$

Multiply -4 times -80.

$$x=\frac{0±\sqrt{320\times 320}}{2\left(-80\right)}$$

Multiply 320 times 320.

$$x=\frac{0±\sqrt{102400}}{2\left(-80\right)}$$

Take the square root of 102400.

$$x=\frac{0±320}{2\left(-80\right)}$$

Multiply 2 times -80.

$$x=\frac{0±320}{-160}$$

Now solve the equation x=\frac{0±320}{-160} when ± is plus. Divide 320 by -160.

$$x=-2$$

Now solve the equation x=\frac{0±320}{-160} when ± is minus. Divide -320 by -160.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$