Solve (1000)^2+(2400)^2=x^2

$$( 1000 ) ^ { 2 } + ( 2400 ) ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=-2600$$

$$x=2600$$

Steps Using Difference of Squares

Calculate 1000 to the power of 2 and get 1000000.

$$1000000+2400^{2}=x^{2}$$

Calculate 2400 to the power of 2 and get 5760000.

$$1000000+5760000=x^{2}$$

Add 1000000 and 5760000 to get 6760000.

$$6760000=x^{2}$$

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

$$x^{2}=6760000$$

Subtract 6760000 from both sides.

$$x^{2}-6760000=0$$

Consider x^{2}-6760000. Rewrite x^{2}-6760000 as x^{2}-2600^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2600\right)\left(x+2600\right)=0$$

To find equation solutions, solve x-2600=0 and x+2600=0.

$$x=2600 x=-2600$$

Steps by Finding Square Root

Calculate 1000 to the power of 2 and get 1000000.

$$1000000+2400^{2}=x^{2}$$

Calculate 2400 to the power of 2 and get 5760000.

$$1000000+5760000=x^{2}$$

Add 1000000 and 5760000 to get 6760000.

$$6760000=x^{2}$$

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

$$x^{2}=6760000$$

Take the square root of both sides of the equation.

$$x=2600 x=-2600$$

Steps Using the Quadratic Formula

Calculate 1000 to the power of 2 and get 1000000.

$$1000000+2400^{2}=x^{2}$$

Calculate 2400 to the power of 2 and get 5760000.

$$1000000+5760000=x^{2}$$

Add 1000000 and 5760000 to get 6760000.

$$6760000=x^{2}$$

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

$$x^{2}=6760000$$

Subtract 6760000 from both sides.

$$x^{2}-6760000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6760000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6760000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6760000\right)}}{2}$$

Multiply -4 times -6760000.

$$x=\frac{0±\sqrt{27040000}}{2}$$

Take the square root of 27040000.

$$x=\frac{0±5200}{2}$$

Now solve the equation x=\frac{0±5200}{2} when ± is plus. Divide 5200 by 2.

$$x=2600$$

Now solve the equation x=\frac{0±5200}{2} when ± is minus. Divide -5200 by 2.

$$x=-2600$$

The equation is now solved.

$$x=2600 x=-2600$$