Solve 0.04n^2-0.25=0

$$0.04 n ^ { 2 } - 0.25 = 0$$

Solve for n

$$n=2.5$$

$$n=-2.5$$

Steps Using Difference of Squares

Consider 0.04n^{2}-0.25. Rewrite \frac{n^{2}}{25}-0.25 as \left(\frac{1}{5}n\right)^{2}-\left(\frac{1}{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(\frac{n}{5}-\frac{1}{2}\right)\left(\frac{n}{5}+\frac{1}{2}\right)=0$$

To find equation solutions, solve \frac{n}{5}-\frac{1}{2}=0 and \frac{n}{5}+\frac{1}{2}=0.

$$n=\frac{5}{2} n=-\frac{5}{2}$$

Steps by Finding Square Root

Add 0.25 to both sides. Anything plus zero gives itself.

$$0.04n^{2}=0.25$$

Divide both sides by 0.04.

$$n^{2}=\frac{0.25}{0.04}$$

Expand \frac{0.25}{0.04} by multiplying both numerator and the denominator by 100.

$$n^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$n=\frac{5}{2} n=-\frac{5}{2}$$

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.

$$0.04n^{2}-0.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.04 for a, 0 for b, and -0.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 0.04\left(-0.25\right)}}{2\times 0.04}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 0.04\left(-0.25\right)}}{2\times 0.04}$$

Multiply -4 times 0.04.

$$n=\frac{0±\sqrt{-0.16\left(-0.25\right)}}{2\times 0.04}$$

Multiply -0.16 times -0.25 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$n=\frac{0±\sqrt{0.04}}{2\times 0.04}$$

Take the square root of 0.04.

$$n=\frac{0±\frac{1}{5}}{2\times 0.04}$$

Multiply 2 times 0.04.

$$n=\frac{0±\frac{1}{5}}{0.08}$$

Now solve the equation n=\frac{0±\frac{1}{5}}{0.08} when ± is plus.

$$n=\frac{5}{2}$$

Now solve the equation n=\frac{0±\frac{1}{5}}{0.08} when ± is minus.

$$n=-\frac{5}{2}$$

The equation is now solved.

$$n=\frac{5}{2} n=-\frac{5}{2}$$