Solve 9^2+12^2=n^2

$$9 ^ { 2 } + 12 ^ { 2 } = n ^ { 2 }$$

Solve for n

$$n=15$$

$$n=-15$$

Steps Using Difference of Squares

Calculate 9 to the power of 2 and get 81.

$$81+12^{2}=n^{2}$$

Calculate 12 to the power of 2 and get 144.

$$81+144=n^{2}$$

Add 81 and 144 to get 225.

$$225=n^{2}$$

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

$$n^{2}=225$$

Subtract 225 from both sides.

$$n^{2}-225=0$$

Consider n^{2}-225. Rewrite n^{2}-225 as n^{2}-15^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-15\right)\left(n+15\right)=0$$

To find equation solutions, solve n-15=0 and n+15=0.

$$n=15 n=-15$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$81+12^{2}=n^{2}$$

Calculate 12 to the power of 2 and get 144.

$$81+144=n^{2}$$

Add 81 and 144 to get 225.

$$225=n^{2}$$

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

$$n^{2}=225$$

Take the square root of both sides of the equation.

$$n=15 n=-15$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$81+12^{2}=n^{2}$$

Calculate 12 to the power of 2 and get 144.

$$81+144=n^{2}$$

Add 81 and 144 to get 225.

$$225=n^{2}$$

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

$$n^{2}=225$$

Subtract 225 from both sides.

$$n^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-225\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-225\right)}}{2}$$

Multiply -4 times -225.

$$n=\frac{0±\sqrt{900}}{2}$$

Take the square root of 900.

$$n=\frac{0±30}{2}$$

Now solve the equation n=\frac{0±30}{2} when ± is plus. Divide 30 by 2.

$$n=15$$

Now solve the equation n=\frac{0±30}{2} when ± is minus. Divide -30 by 2.

$$n=-15$$

The equation is now solved.

$$n=15 n=-15$$