Solve 44=p^2(2p^2+3)

$$44 = p ^ { 2 } ( 2 p ^ { 2 } + 3 )$$

Solve for p

$$p=-2$$

$$p=2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply p^{2} by 2p^{2}+3.

$$44=2p^{4}+3p^{2}$$

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

$$2p^{4}+3p^{2}=44$$

Subtract 44 from both sides.

$$2p^{4}+3p^{2}-44=0$$

Substitute t for p^{2}.

$$2t^{2}+3t-44=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 2 for a, 3 for b, and -44 for c in the quadratic formula.

$$t=\frac{-3±\sqrt{3^{2}-4\times 2\left(-44\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{-3±19}{4}$$

Solve the equation t=\frac{-3±19}{4} when ± is plus and when ± is minus.

$$t=4 t=-\frac{11}{2}$$

Since p=t^{2}, the solutions are obtained by evaluating p=±\sqrt{t} for positive t.

$$p=2 p=-2$$