Solve 100^2+100+8=3p^2-190+11

$$100 ^ { 2 } + 100 + 8 = 3 p ^ { 2 } - 190 + 11$$

Solve for p

$$p=3\sqrt{381}\approx 58.557663888$$

$$p=-3\sqrt{381}\approx -58.557663888$$

Steps by Finding Square Root

Calculate 100 to the power of 2 and get 10000.

$$10000+100+8=3p^{2}-190+11$$

Add 10000 and 100 to get 10100.

$$10100+8=3p^{2}-190+11$$

Add 10100 and 8 to get 10108.

$$10108=3p^{2}-190+11$$

Add -190 and 11 to get -179.

$$10108=3p^{2}-179$$

Swap sides so that all variable terms are on the left hand side.

$$3p^{2}-179=10108$$

Add 179 to both sides.

$$3p^{2}=10108+179$$

Add 10108 and 179 to get 10287.

$$3p^{2}=10287$$

Divide both sides by 3.

$$p^{2}=\frac{10287}{3}$$

Divide 10287 by 3 to get 3429.

$$p^{2}=3429$$

Take the square root of both sides of the equation.

$$p=3\sqrt{381} p=-3\sqrt{381}$$

Steps Using the Quadratic Formula

Calculate 100 to the power of 2 and get 10000.

$$10000+100+8=3p^{2}-190+11$$

Add 10000 and 100 to get 10100.

$$10100+8=3p^{2}-190+11$$

Add 10100 and 8 to get 10108.

$$10108=3p^{2}-190+11$$

Add -190 and 11 to get -179.

$$10108=3p^{2}-179$$

Swap sides so that all variable terms are on the left hand side.

$$3p^{2}-179=10108$$

Subtract 10108 from both sides.

$$3p^{2}-179-10108=0$$

Subtract 10108 from -179 to get -10287.

$$3p^{2}-10287=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -10287 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 3\left(-10287\right)}}{2\times 3}$$

Square 0.

$$p=\frac{0±\sqrt{-4\times 3\left(-10287\right)}}{2\times 3}$$

Multiply -4 times 3.

$$p=\frac{0±\sqrt{-12\left(-10287\right)}}{2\times 3}$$

Multiply -12 times -10287.

$$p=\frac{0±\sqrt{123444}}{2\times 3}$$

Take the square root of 123444.

$$p=\frac{0±18\sqrt{381}}{2\times 3}$$

Multiply 2 times 3.

$$p=\frac{0±18\sqrt{381}}{6}$$

Now solve the equation p=\frac{0±18\sqrt{381}}{6} when ± is plus.

$$p=3\sqrt{381}$$

Now solve the equation p=\frac{0±18\sqrt{381}}{6} when ± is minus.

$$p=-3\sqrt{381}$$

The equation is now solved.

$$p=3\sqrt{381} p=-3\sqrt{381}$$