Solve 10t^4+t^2-10t^2-720=0

$$10 t ^ { 4 } + t ^ { 2 } - 10 t ^ { 2 } - 720 = 0$$

Solve for t

$$t = -\frac{\sqrt{15 {(\sqrt{3209} + 3)}}}{10} \approx -2.991187962$$

$$t = \frac{\sqrt{15 {(\sqrt{3209} + 3)}}}{10} \approx 2.991187962$$

Steps Using the Quadratic Formula

Combine t^{2} and -10t^{2} to get -9t^{2}.

$$10t^{4}-9t^{2}-720=0$$

Substitute t for t^{2}.

$$10t^{2}-9t-720=0$$

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 10 for a, -9 for b, and -720 for c in the quadratic formula.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 10\left(-720\right)}}{2\times 10}$$

Do the calculations.

$$t=\frac{9±3\sqrt{3209}}{20}$$

Solve the equation t=\frac{9±3\sqrt{3209}}{20} when ± is plus and when ± is minus.

$$t=\frac{3\sqrt{3209}+9}{20} t=\frac{9-3\sqrt{3209}}{20}$$

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

$$t=\frac{\sqrt{\frac{3\sqrt{3209}+9}{5}}}{2} t=-\frac{\sqrt{\frac{3\sqrt{3209}+9}{5}}}{2}$$