Solve 120*200=x^2-120^2-200^2

$$120 \times 200 = x ^ { 2 } - 120 ^ { 2 } - 200 ^ { 2 }$$

Solve for x

$$x=280$$

$$x=-280$$

Steps Using Difference of Squares

Multiply 120 and 200 to get 24000.

$$24000=x^{2}-120^{2}-200^{2}$$

Calculate 120 to the power of 2 and get 14400.

$$24000=x^{2}-14400-200^{2}$$

Calculate 200 to the power of 2 and get 40000.

$$24000=x^{2}-14400-40000$$

Subtract 40000 from -14400 to get -54400.

$$24000=x^{2}-54400$$

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

$$x^{2}-54400=24000$$

Subtract 24000 from both sides.

$$x^{2}-54400-24000=0$$

Subtract 24000 from -54400 to get -78400.

$$x^{2}-78400=0$$

Consider x^{2}-78400. Rewrite x^{2}-78400 as x^{2}-280^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-280\right)\left(x+280\right)=0$$

To find equation solutions, solve x-280=0 and x+280=0.

$$x=280 x=-280$$

Steps by Finding Square Root

Multiply 120 and 200 to get 24000.

$$24000=x^{2}-120^{2}-200^{2}$$

Calculate 120 to the power of 2 and get 14400.

$$24000=x^{2}-14400-200^{2}$$

Calculate 200 to the power of 2 and get 40000.

$$24000=x^{2}-14400-40000$$

Subtract 40000 from -14400 to get -54400.

$$24000=x^{2}-54400$$

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

$$x^{2}-54400=24000$$

Add 54400 to both sides.

$$x^{2}=24000+54400$$

Add 24000 and 54400 to get 78400.

$$x^{2}=78400$$

Take the square root of both sides of the equation.

$$x=280 x=-280$$

Steps Using the Quadratic Formula

Multiply 120 and 200 to get 24000.

$$24000=x^{2}-120^{2}-200^{2}$$

Calculate 120 to the power of 2 and get 14400.

$$24000=x^{2}-14400-200^{2}$$

Calculate 200 to the power of 2 and get 40000.

$$24000=x^{2}-14400-40000$$

Subtract 40000 from -14400 to get -54400.

$$24000=x^{2}-54400$$

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

$$x^{2}-54400=24000$$

Subtract 24000 from both sides.

$$x^{2}-54400-24000=0$$

Subtract 24000 from -54400 to get -78400.

$$x^{2}-78400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -78400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-78400\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-78400\right)}}{2}$$

Multiply -4 times -78400.

$$x=\frac{0±\sqrt{313600}}{2}$$

Take the square root of 313600.

$$x=\frac{0±560}{2}$$

Now solve the equation x=\frac{0±560}{2} when ± is plus. Divide 560 by 2.

$$x=280$$

Now solve the equation x=\frac{0±560}{2} when ± is minus. Divide -560 by 2.

$$x=-280$$

The equation is now solved.

$$x=280 x=-280$$