Solve 2n^2=72

$$2 n ^ { 2 } = 72$$

Solve for n

$$n=6$$

$$n=-6$$

Steps Using Difference of Squares

Divide both sides by 2.

$$n^{2}=\frac{72}{2}$$

Divide 72 by 2 to get 36.

$$n^{2}=36$$

Subtract 36 from both sides.

$$n^{2}-36=0$$

Consider n^{2}-36. Rewrite n^{2}-36 as n^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-6\right)\left(n+6\right)=0$$

To find equation solutions, solve n-6=0 and n+6=0.

$$n=6 n=-6$$

Steps by Finding Square Root

Divide both sides by 2.

$$n^{2}=\frac{72}{2}$$

Divide 72 by 2 to get 36.

$$n^{2}=36$$

Take the square root of both sides of the equation.

$$n=6 n=-6$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$n^{2}=\frac{72}{2}$$

Divide 72 by 2 to get 36.

$$n^{2}=36$$

Subtract 36 from both sides.

$$n^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$n=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$n=\frac{0±12}{2}$$

Now solve the equation n=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$n=6$$

Now solve the equation n=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$n=-6$$

The equation is now solved.

$$n=6 n=-6$$