Solve x^4-784x^2+57600=0

$${ x }^{ 4 } -784 { x }^{ 2 } +57600=0$$

Solve for x

$$x=2\left(\sqrt{19}-\sqrt{79}\right)\approx -9.058590948$$

$$x=2\left(\sqrt{79}-\sqrt{19}\right)\approx 9.058590948$$

$$x=2\left(\sqrt{19}+\sqrt{79}\right)\approx 26.494186722$$

$$x=2\left(-\sqrt{19}-\sqrt{79}\right)\approx -26.494186722$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-784t+57600=0$$

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 1 for a, -784 for b, and 57600 for c in the quadratic formula.

$$t=\frac{-\left(-784\right)±\sqrt{\left(-784\right)^{2}-4\times 1\times 57600}}{2}$$

Do the calculations.

$$t=\frac{784±16\sqrt{1501}}{2}$$

Solve the equation t=\frac{784±16\sqrt{1501}}{2} when ± is plus and when ± is minus.

$$t=8\sqrt{1501}+392 t=392-8\sqrt{1501}$$

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

$$x=2\sqrt{19}+2\sqrt{79} x=-\left(2\sqrt{19}+2\sqrt{79}\right) x=-\left(2\sqrt{19}-2\sqrt{79}\right) x=2\sqrt{19}-2\sqrt{79}$$