Solve left(1800+xright)left(x-800right)=left(1800-xright)left(800+xright)

$$\left( 1800+x \right) \left( x-800 \right) = \left( 1800-x \right) \left( 800+x \right)$$

Solve for x

$$x=-1200$$

$$x=1200$$

Steps by Finding Square Root

Use the distributive property to multiply 1800+x by x-800 and combine like terms.

$$1000x-1440000+x^{2}=\left(1800-x\right)\left(800+x\right)$$

Use the distributive property to multiply 1800-x by 800+x and combine like terms.

$$1000x-1440000+x^{2}=1440000+1000x-x^{2}$$

Subtract 1000x from both sides.

$$1000x-1440000+x^{2}-1000x=1440000-x^{2}$$

Combine 1000x and -1000x to get 0.

$$-1440000+x^{2}=1440000-x^{2}$$

Add x^{2} to both sides.

$$-1440000+x^{2}+x^{2}=1440000$$

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

$$-1440000+2x^{2}=1440000$$

Add 1440000 to both sides.

$$2x^{2}=1440000+1440000$$

Add 1440000 and 1440000 to get 2880000.

$$2x^{2}=2880000$$

Divide both sides by 2.

$$x^{2}=\frac{2880000}{2}$$

Divide 2880000 by 2 to get 1440000.

$$x^{2}=1440000$$

Take the square root of both sides of the equation.

$$x=1200 x=-1200$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 1800+x by x-800 and combine like terms.

$$1000x-1440000+x^{2}=\left(1800-x\right)\left(800+x\right)$$

Use the distributive property to multiply 1800-x by 800+x and combine like terms.

$$1000x-1440000+x^{2}=1440000+1000x-x^{2}$$

Subtract 1440000 from both sides.

$$1000x-1440000+x^{2}-1440000=1000x-x^{2}$$

Subtract 1440000 from -1440000 to get -2880000.

$$1000x-2880000+x^{2}=1000x-x^{2}$$

Subtract 1000x from both sides.

$$1000x-2880000+x^{2}-1000x=-x^{2}$$

Combine 1000x and -1000x to get 0.

$$-2880000+x^{2}=-x^{2}$$

Add x^{2} to both sides.

$$-2880000+x^{2}+x^{2}=0$$

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

$$-2880000+2x^{2}=0$$

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.

$$2x^{2}-2880000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -2880000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-2880000\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-2880000\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-2880000\right)}}{2\times 2}$$

Multiply -8 times -2880000.

$$x=\frac{0±\sqrt{23040000}}{2\times 2}$$

Take the square root of 23040000.

$$x=\frac{0±4800}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4800}{4}$$

Now solve the equation x=\frac{0±4800}{4} when ± is plus. Divide 4800 by 4.

$$x=1200$$

Now solve the equation x=\frac{0±4800}{4} when ± is minus. Divide -4800 by 4.

$$x=-1200$$

The equation is now solved.

$$x=1200 x=-1200$$