Solve N^2-0.750+0.135=0

$$N ^ { 2 } - 0.750 + 0.135 = 0$$

Solve for N

$$N=\frac{\sqrt{246}}{20}\approx 0.784219357$$

$$N=-\frac{\sqrt{246}}{20}\approx -0.784219357$$

Steps by Finding Square Root

Add -0.75 and 0.135 to get -0.615.

$$N^{2}-0.615=0$$

Add 0.615 to both sides. Anything plus zero gives itself.

$$N^{2}=0.615$$

Take the square root of both sides of the equation.

$$N=\frac{\sqrt{246}}{20} N=-\frac{\sqrt{246}}{20}$$

Steps Using the Quadratic Formula

Add -0.75 and 0.135 to get -0.615.

$$N^{2}-0.615=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -0.615 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$N=\frac{0±\sqrt{0^{2}-4\left(-0.615\right)}}{2}$$

Square 0.

$$N=\frac{0±\sqrt{-4\left(-0.615\right)}}{2}$$

Multiply -4 times -0.615.

$$N=\frac{0±\sqrt{2.46}}{2}$$

Take the square root of 2.46.

$$N=\frac{0±\frac{\sqrt{246}}{10}}{2}$$

Now solve the equation N=\frac{0±\frac{\sqrt{246}}{10}}{2} when ± is plus.

$$N=\frac{\sqrt{246}}{20}$$

Now solve the equation N=\frac{0±\frac{\sqrt{246}}{10}}{2} when ± is minus.

$$N=-\frac{\sqrt{246}}{20}$$

The equation is now solved.

$$N=\frac{\sqrt{246}}{20} N=-\frac{\sqrt{246}}{20}$$