Solve 6^2+8^2=c^2

$$6 ^ { 2 } + 8 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=10$$

$$c=-10$$

Steps Using Difference of Squares

Calculate 6 to the power of 2 and get 36.

$$36+8^{2}=c^{2}$$

Calculate 8 to the power of 2 and get 64.

$$36+64=c^{2}$$

Add 36 and 64 to get 100.

$$100=c^{2}$$

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

$$c^{2}=100$$

Subtract 100 from both sides.

$$c^{2}-100=0$$

Consider c^{2}-100. Rewrite c^{2}-100 as c^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-10\right)\left(c+10\right)=0$$

To find equation solutions, solve c-10=0 and c+10=0.

$$c=10 c=-10$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36+8^{2}=c^{2}$$

Calculate 8 to the power of 2 and get 64.

$$36+64=c^{2}$$

Add 36 and 64 to get 100.

$$100=c^{2}$$

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

$$c^{2}=100$$

Take the square root of both sides of the equation.

$$c=10 c=-10$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36+8^{2}=c^{2}$$

Calculate 8 to the power of 2 and get 64.

$$36+64=c^{2}$$

Add 36 and 64 to get 100.

$$100=c^{2}$$

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

$$c^{2}=100$$

Subtract 100 from both sides.

$$c^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-100\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-100\right)}}{2}$$

Multiply -4 times -100.

$$c=\frac{0±\sqrt{400}}{2}$$

Take the square root of 400.

$$c=\frac{0±20}{2}$$

Now solve the equation c=\frac{0±20}{2} when ± is plus. Divide 20 by 2.

$$c=10$$

Now solve the equation c=\frac{0±20}{2} when ± is minus. Divide -20 by 2.

$$c=-10$$

The equation is now solved.

$$c=10 c=-10$$