Solve n^2-121=0?

$$n ^ { 2 } - 121 = 0 ?$$

Solve for n

$$n=11$$

$$n=-11$$

Steps Using Difference of Squares

Consider n^{2}-121. Rewrite n^{2}-121 as n^{2}-11^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-11\right)\left(n+11\right)=0$$

To find equation solutions, solve n-11=0 and n+11=0.

$$n=11 n=-11$$

Steps by Finding Square Root

Add 121 to both sides. Anything plus zero gives itself.

$$n^{2}=121$$

Take the square root of both sides of the equation.

$$n=11 n=-11$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$n^{2}-121=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -121 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-121\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-121\right)}}{2}$$

Multiply -4 times -121.

$$n=\frac{0±\sqrt{484}}{2}$$

Take the square root of 484.

$$n=\frac{0±22}{2}$$

Now solve the equation n=\frac{0±22}{2} when ± is plus. Divide 22 by 2.

$$n=11$$

Now solve the equation n=\frac{0±22}{2} when ± is minus. Divide -22 by 2.

$$n=-11$$

The equation is now solved.

$$n=11 n=-11$$