Solve n^2-5=0

$$n ^ { 2 } - 5 = 0$$

Solve for n

$$n=\sqrt{5}\approx 2.236067977$$

$$n=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Add 5 to both sides. Anything plus zero gives itself.

$$n^{2}=5$$

Take the square root of both sides of the equation.

$$n=\sqrt{5} n=-\sqrt{5}$$

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.

$$n^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-5\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-5\right)}}{2}$$

Multiply -4 times -5.

$$n=\frac{0±\sqrt{20}}{2}$$

Take the square root of 20.

$$n=\frac{0±2\sqrt{5}}{2}$$

Now solve the equation n=\frac{0±2\sqrt{5}}{2} when ± is plus.

$$n=\sqrt{5}$$

Now solve the equation n=\frac{0±2\sqrt{5}}{2} when ± is minus.

$$n=-\sqrt{5}$$

The equation is now solved.

$$n=\sqrt{5} n=-\sqrt{5}$$