Solve 10^2+24^2=c^2

$$10 ^ { 2 } + 24 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=26$$

$$c=-26$$

Steps Using Difference of Squares

Calculate 10 to the power of 2 and get 100.

$$100+24^{2}=c^{2}$$

Calculate 24 to the power of 2 and get 576.

$$100+576=c^{2}$$

Add 100 and 576 to get 676.

$$676=c^{2}$$

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

$$c^{2}=676$$

Subtract 676 from both sides.

$$c^{2}-676=0$$

Consider c^{2}-676. Rewrite c^{2}-676 as c^{2}-26^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-26\right)\left(c+26\right)=0$$

To find equation solutions, solve c-26=0 and c+26=0.

$$c=26 c=-26$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100+24^{2}=c^{2}$$

Calculate 24 to the power of 2 and get 576.

$$100+576=c^{2}$$

Add 100 and 576 to get 676.

$$676=c^{2}$$

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

$$c^{2}=676$$

Take the square root of both sides of the equation.

$$c=26 c=-26$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100+24^{2}=c^{2}$$

Calculate 24 to the power of 2 and get 576.

$$100+576=c^{2}$$

Add 100 and 576 to get 676.

$$676=c^{2}$$

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

$$c^{2}=676$$

Subtract 676 from both sides.

$$c^{2}-676=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -676 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-676\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-676\right)}}{2}$$

Multiply -4 times -676.

$$c=\frac{0±\sqrt{2704}}{2}$$

Take the square root of 2704.

$$c=\frac{0±52}{2}$$

Now solve the equation c=\frac{0±52}{2} when ± is plus. Divide 52 by 2.

$$c=26$$

Now solve the equation c=\frac{0±52}{2} when ± is minus. Divide -52 by 2.

$$c=-26$$

The equation is now solved.

$$c=26 c=-26$$