Solve 45^2+50^2=c^2

$$45 ^ { 2 } + 50 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=5\sqrt{181}\approx 67.268120235$$

$$c=-5\sqrt{181}\approx -67.268120235$$

Steps by Finding Square Root

Calculate 45 to the power of 2 and get 2025.

$$2025+50^{2}=c^{2}$$

Calculate 50 to the power of 2 and get 2500.

$$2025+2500=c^{2}$$

Add 2025 and 2500 to get 4525.

$$4525=c^{2}$$

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

$$c^{2}=4525$$

Take the square root of both sides of the equation.

$$c=5\sqrt{181} c=-5\sqrt{181}$$

Steps Using the Quadratic Formula

Calculate 45 to the power of 2 and get 2025.

$$2025+50^{2}=c^{2}$$

Calculate 50 to the power of 2 and get 2500.

$$2025+2500=c^{2}$$

Add 2025 and 2500 to get 4525.

$$4525=c^{2}$$

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

$$c^{2}=4525$$

Subtract 4525 from both sides.

$$c^{2}-4525=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4525 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-4525\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-4525\right)}}{2}$$

Multiply -4 times -4525.

$$c=\frac{0±\sqrt{18100}}{2}$$

Take the square root of 18100.

$$c=\frac{0±10\sqrt{181}}{2}$$

Now solve the equation c=\frac{0±10\sqrt{181}}{2} when ± is plus.

$$c=5\sqrt{181}$$

Now solve the equation c=\frac{0±10\sqrt{181}}{2} when ± is minus.

$$c=-5\sqrt{181}$$

The equation is now solved.

$$c=5\sqrt{181} c=-5\sqrt{181}$$