Solve 4x^4-33x^2+50=0

$$4 x ^ { 4 } - 33 x ^ { 2 } + 50 = 0$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$4t^{2}-33t+50=0$$

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 4 for a, -33 for b, and 50 for c in the quadratic formula.

$$t=\frac{-\left(-33\right)±\sqrt{\left(-33\right)^{2}-4\times 4\times 50}}{2\times 4}$$

Do the calculations.

$$t=\frac{33±17}{8}$$

Solve the equation t=\frac{33±17}{8} when ± is plus and when ± is minus.

$$t=\frac{25}{4} t=2$$

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

$$x=\frac{5}{2} x=-\frac{5}{2} x=\sqrt{2} x=-\sqrt{2}$$