Solve -n^2+12=3

$$- n ^ { 2 } + 12 = 3$$

Solve for n

$$n=3$$

$$n=-3$$

Steps by Finding Square Root

Subtract 12 from both sides.

$$-n^{2}=3-12$$

Subtract 12 from 3 to get -9.

$$-n^{2}=-9$$

Divide both sides by -1.

$$n^{2}=\frac{-9}{-1}$$

Fraction \frac{-9}{-1} can be simplified to 9 by removing the negative sign from both the numerator and the denominator.

$$n^{2}=9$$

Take the square root of both sides of the equation.

$$n=3 n=-3$$

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$-n^{2}+12-3=0$$

Subtract 3 from 12 to get 9.

$$-n^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 9}}{2\left(-1\right)}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-1\right)\times 9}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$n=\frac{0±\sqrt{4\times 9}}{2\left(-1\right)}$$

Multiply 4 times 9.

$$n=\frac{0±\sqrt{36}}{2\left(-1\right)}$$

Take the square root of 36.

$$n=\frac{0±6}{2\left(-1\right)}$$

Multiply 2 times -1.

$$n=\frac{0±6}{-2}$$

Now solve the equation n=\frac{0±6}{-2} when ± is plus. Divide 6 by -2.

$$n=-3$$

Now solve the equation n=\frac{0±6}{-2} when ± is minus. Divide -6 by -2.

$$n=3$$

The equation is now solved.

$$n=-3 n=3$$