Solve c^2=45^2+96^2

$${ c }^{ 2 } = { 45 }^{ 2 } + { 96 }^{ 2 }$$

Solve for c

$$c=3\sqrt{1249}\approx 106.023582282$$

$$c=-3\sqrt{1249}\approx -106.023582282$$

Steps by Finding Square Root

Calculate 45 to the power of 2 and get 2025.

$$c^{2}=2025+96^{2}$$

Calculate 96 to the power of 2 and get 9216.

$$c^{2}=2025+9216$$

Add 2025 and 9216 to get 11241.

$$c^{2}=11241$$

Take the square root of both sides of the equation.

$$c=3\sqrt{1249} c=-3\sqrt{1249}$$

Steps Using the Quadratic Formula

Calculate 45 to the power of 2 and get 2025.

$$c^{2}=2025+96^{2}$$

Calculate 96 to the power of 2 and get 9216.

$$c^{2}=2025+9216$$

Add 2025 and 9216 to get 11241.

$$c^{2}=11241$$

Subtract 11241 from both sides.

$$c^{2}-11241=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -11241 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-11241\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-11241\right)}}{2}$$

Multiply -4 times -11241.

$$c=\frac{0±\sqrt{44964}}{2}$$

Take the square root of 44964.

$$c=\frac{0±6\sqrt{1249}}{2}$$

Now solve the equation c=\frac{0±6\sqrt{1249}}{2} when ± is plus.

$$c=3\sqrt{1249}$$

Now solve the equation c=\frac{0±6\sqrt{1249}}{2} when ± is minus.

$$c=-3\sqrt{1249}$$

The equation is now solved.

$$c=3\sqrt{1249} c=-3\sqrt{1249}$$