Solve 450^2+250^2=c^2

$$450 ^ { 2 } + 250 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=50\sqrt{106}\approx 514.781507049$$

$$c=-50\sqrt{106}\approx -514.781507049$$

Steps by Finding Square Root

Calculate 450 to the power of 2 and get 202500.

$$202500+250^{2}=c^{2}$$

Calculate 250 to the power of 2 and get 62500.

$$202500+62500=c^{2}$$

Add 202500 and 62500 to get 265000.

$$265000=c^{2}$$

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

$$c^{2}=265000$$

Take the square root of both sides of the equation.

$$c=50\sqrt{106} c=-50\sqrt{106}$$

Steps Using the Quadratic Formula

Calculate 450 to the power of 2 and get 202500.

$$202500+250^{2}=c^{2}$$

Calculate 250 to the power of 2 and get 62500.

$$202500+62500=c^{2}$$

Add 202500 and 62500 to get 265000.

$$265000=c^{2}$$

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

$$c^{2}=265000$$

Subtract 265000 from both sides.

$$c^{2}-265000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -265000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-265000\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-265000\right)}}{2}$$

Multiply -4 times -265000.

$$c=\frac{0±\sqrt{1060000}}{2}$$

Take the square root of 1060000.

$$c=\frac{0±100\sqrt{106}}{2}$$

Now solve the equation c=\frac{0±100\sqrt{106}}{2} when ± is plus.

$$c=50\sqrt{106}$$

Now solve the equation c=\frac{0±100\sqrt{106}}{2} when ± is minus.

$$c=-50\sqrt{106}$$

The equation is now solved.

$$c=50\sqrt{106} c=-50\sqrt{106}$$