Solve 7^2+24^2=c_2^2

$$7 ^ { 2 } + 24 ^ { 2 } = c _ { 2 } ^ { 2 }$$

Solve for c_2

$$c_{2}=25$$

$$c_{2}=-25$$

Steps Using Difference of Squares

Calculate 7 to the power of 2 and get 49.

$$49+24^{2}=c_{2}^{2}$$

Calculate 24 to the power of 2 and get 576.

$$49+576=c_{2}^{2}$$

Add 49 and 576 to get 625.

$$625=c_{2}^{2}$$

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

$$c_{2}^{2}=625$$

Subtract 625 from both sides.

$$c_{2}^{2}-625=0$$

Consider c_{2}^{2}-625. Rewrite c_{2}^{2}-625 as c_{2}^{2}-25^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c_{2}-25\right)\left(c_{2}+25\right)=0$$

To find equation solutions, solve c_{2}-25=0 and c_{2}+25=0.

$$c_{2}=25 c_{2}=-25$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$49+24^{2}=c_{2}^{2}$$

Calculate 24 to the power of 2 and get 576.

$$49+576=c_{2}^{2}$$

Add 49 and 576 to get 625.

$$625=c_{2}^{2}$$

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

$$c_{2}^{2}=625$$

Take the square root of both sides of the equation.

$$c_{2}=25 c_{2}=-25$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$49+24^{2}=c_{2}^{2}$$

Calculate 24 to the power of 2 and get 576.

$$49+576=c_{2}^{2}$$

Add 49 and 576 to get 625.

$$625=c_{2}^{2}$$

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

$$c_{2}^{2}=625$$

Subtract 625 from both sides.

$$c_{2}^{2}-625=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -625 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c_{2}=\frac{0±\sqrt{0^{2}-4\left(-625\right)}}{2}$$

Square 0.

$$c_{2}=\frac{0±\sqrt{-4\left(-625\right)}}{2}$$

Multiply -4 times -625.

$$c_{2}=\frac{0±\sqrt{2500}}{2}$$

Take the square root of 2500.

$$c_{2}=\frac{0±50}{2}$$

Now solve the equation c_{2}=\frac{0±50}{2} when ± is plus. Divide 50 by 2.

$$c_{2}=25$$

Now solve the equation c_{2}=\frac{0±50}{2} when ± is minus. Divide -50 by 2.

$$c_{2}=-25$$

The equation is now solved.

$$c_{2}=25 c_{2}=-25$$