Solve 4x^4-21x^2+20=0

$$4 x ^ { 4 } - 21 x ^ { 2 } + 20 = 0$$

Solve for x

$$x = -\frac{\sqrt{5}}{2} \approx -1.118033989$$

$$x = \frac{\sqrt{5}}{2} \approx 1.118033989$$

$$x=2$$

$$x=-2$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$4t^{2}-21t+20=0$$

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, -21 for b, and 20 for c in the quadratic formula.

$$t=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 4\times 20}}{2\times 4}$$

Do the calculations.

$$t=\frac{21±11}{8}$$

Solve the equation t=\frac{21±11}{8} when ± is plus and when ± is minus.

$$t=4 t=\frac{5}{4}$$

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

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