Solve 9-6n^2=-555

$$9 - 6 n ^ { 2 } = - 555$$

Solve for n

$$n=\sqrt{94}\approx 9.695359715$$

$$n=-\sqrt{94}\approx -9.695359715$$

Steps by Finding Square Root

Subtract 9 from both sides.

$$-6n^{2}=-555-9$$

Subtract 9 from -555 to get -564.

$$-6n^{2}=-564$$

Divide both sides by -6.

$$n^{2}=\frac{-564}{-6}$$

Divide -564 by -6 to get 94.

$$n^{2}=94$$

Take the square root of both sides of the equation.

$$n=\sqrt{94} n=-\sqrt{94}$$

Steps Using the Quadratic Formula

Add 555 to both sides.

$$9-6n^{2}+555=0$$

Add 9 and 555 to get 564.

$$564-6n^{2}=0$$

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.

$$-6n^{2}+564=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 564 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 564}}{2\left(-6\right)}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-6\right)\times 564}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$n=\frac{0±\sqrt{24\times 564}}{2\left(-6\right)}$$

Multiply 24 times 564.

$$n=\frac{0±\sqrt{13536}}{2\left(-6\right)}$$

Take the square root of 13536.

$$n=\frac{0±12\sqrt{94}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$n=\frac{0±12\sqrt{94}}{-12}$$

Now solve the equation n=\frac{0±12\sqrt{94}}{-12} when ± is plus.

$$n=-\sqrt{94}$$

Now solve the equation n=\frac{0±12\sqrt{94}}{-12} when ± is minus.

$$n=\sqrt{94}$$

The equation is now solved.

$$n=-\sqrt{94} n=\sqrt{94}$$