Solve 2x^4-50x^2+288=0

$$2 x ^ { 4 } - 50 x ^ { 2 } + 288 = 0$$

Solve for x

$$x=-4$$

$$x=4$$

$$x=3$$

$$x=-3$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$2t^{2}-50t+288=0$$

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, -50 for b, and 288 for c in the quadratic formula.

$$t=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 2\times 288}}{2\times 2}$$

Do the calculations.

$$t=\frac{50±14}{4}$$

Solve the equation t=\frac{50±14}{4} when ± is plus and when ± is minus.

$$t=16 t=9$$

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

$$x=4 x=-4 x=3 x=-3$$