Solve 35^2+12^2=c^2

$$35 ^ { 2 } + 12 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=37$$

$$c=-37$$

Steps Using Difference of Squares

Calculate 35 to the power of 2 and get 1225.

$$1225+12^{2}=c^{2}$$

Calculate 12 to the power of 2 and get 144.

$$1225+144=c^{2}$$

Add 1225 and 144 to get 1369.

$$1369=c^{2}$$

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

$$c^{2}=1369$$

Subtract 1369 from both sides.

$$c^{2}-1369=0$$

Consider c^{2}-1369. Rewrite c^{2}-1369 as c^{2}-37^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-37\right)\left(c+37\right)=0$$

To find equation solutions, solve c-37=0 and c+37=0.

$$c=37 c=-37$$

Steps by Finding Square Root

Calculate 35 to the power of 2 and get 1225.

$$1225+12^{2}=c^{2}$$

Calculate 12 to the power of 2 and get 144.

$$1225+144=c^{2}$$

Add 1225 and 144 to get 1369.

$$1369=c^{2}$$

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

$$c^{2}=1369$$

Take the square root of both sides of the equation.

$$c=37 c=-37$$

Steps Using the Quadratic Formula

Calculate 35 to the power of 2 and get 1225.

$$1225+12^{2}=c^{2}$$

Calculate 12 to the power of 2 and get 144.

$$1225+144=c^{2}$$

Add 1225 and 144 to get 1369.

$$1369=c^{2}$$

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

$$c^{2}=1369$$

Subtract 1369 from both sides.

$$c^{2}-1369=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1369 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1369\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1369\right)}}{2}$$

Multiply -4 times -1369.

$$c=\frac{0±\sqrt{5476}}{2}$$

Take the square root of 5476.

$$c=\frac{0±74}{2}$$

Now solve the equation c=\frac{0±74}{2} when ± is plus. Divide 74 by 2.

$$c=37$$

Now solve the equation c=\frac{0±74}{2} when ± is minus. Divide -74 by 2.

$$c=-37$$

The equation is now solved.

$$c=37 c=-37$$