Solve n^2-60=4

$$n ^ { 2 } - 60 = 4$$

Solve for n

$$n=8$$

$$n=-8$$

Steps Using Difference of Squares

Subtract 4 from both sides.

$$n^{2}-60-4=0$$

Subtract 4 from -60 to get -64.

$$n^{2}-64=0$$

Consider n^{2}-64. Rewrite n^{2}-64 as n^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-8\right)\left(n+8\right)=0$$

To find equation solutions, solve n-8=0 and n+8=0.

$$n=8 n=-8$$

Steps by Finding Square Root

Add 60 to both sides.

$$n^{2}=4+60$$

Add 4 and 60 to get 64.

$$n^{2}=64$$

Take the square root of both sides of the equation.

$$n=8 n=-8$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$n^{2}-60-4=0$$

Subtract 4 from -60 to get -64.

$$n^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$n=\frac{0±\sqrt{256}}{2}$$

Take the square root of 256.

$$n=\frac{0±16}{2}$$

Now solve the equation n=\frac{0±16}{2} when ± is plus. Divide 16 by 2.

$$n=8$$

Now solve the equation n=\frac{0±16}{2} when ± is minus. Divide -16 by 2.

$$n=-8$$

The equation is now solved.

$$n=8 n=-8$$