Solve 9p^2+2=551

$$9 p ^ { 2 } + 2 = 551$$

Solve for p

$$p=\sqrt{61}\approx 7.810249676$$

$$p=-\sqrt{61}\approx -7.810249676$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$9p^{2}=551-2$$

Subtract 2 from 551 to get 549.

$$9p^{2}=549$$

Divide both sides by 9.

$$p^{2}=\frac{549}{9}$$

Divide 549 by 9 to get 61.

$$p^{2}=61$$

Take the square root of both sides of the equation.

$$p=\sqrt{61} p=-\sqrt{61}$$

Steps Using the Quadratic Formula

Subtract 551 from both sides.

$$9p^{2}+2-551=0$$

Subtract 551 from 2 to get -549.

$$9p^{2}-549=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -549 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 9\left(-549\right)}}{2\times 9}$$

Square 0.

$$p=\frac{0±\sqrt{-4\times 9\left(-549\right)}}{2\times 9}$$

Multiply -4 times 9.

$$p=\frac{0±\sqrt{-36\left(-549\right)}}{2\times 9}$$

Multiply -36 times -549.

$$p=\frac{0±\sqrt{19764}}{2\times 9}$$

Take the square root of 19764.

$$p=\frac{0±18\sqrt{61}}{2\times 9}$$

Multiply 2 times 9.

$$p=\frac{0±18\sqrt{61}}{18}$$

Now solve the equation p=\frac{0±18\sqrt{61}}{18} when ± is plus.

$$p=\sqrt{61}$$

Now solve the equation p=\frac{0±18\sqrt{61}}{18} when ± is minus.

$$p=-\sqrt{61}$$

The equation is now solved.

$$p=\sqrt{61} p=-\sqrt{61}$$