Solve 33t^4+1826t^2-750779=0

$$33 t ^ { 4 } + 1826 t ^ { 2 } - 750779 = 0$$

Solve for t (complex solution)

$$t=\frac{i\sqrt{66\sqrt{6402319}+30129}}{33}\approx 13.45425565i$$

$$t=-\frac{i\sqrt{66\sqrt{6402319}+30129}}{33}\approx -0-13.45425565i$$

$$t = -\frac{\sqrt{66 \sqrt{6402319} - 30129}}{33} \approx -11.21087248$$

$$t = \frac{\sqrt{66 \sqrt{6402319} - 30129}}{33} \approx 11.21087248$$

Steps Using the Quadratic Formula

Substitute t for t^{2}.

$$33t^{2}+1826t-750779=0$$

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 33 for a, 1826 for b, and -750779 for c in the quadratic formula.

$$t=\frac{-1826±\sqrt{1826^{2}-4\times 33\left(-750779\right)}}{2\times 33}$$

Do the calculations.

$$t=\frac{-1826±4\sqrt{6402319}}{66}$$

Solve the equation t=\frac{-1826±4\sqrt{6402319}}{66} when ± is plus and when ± is minus.

$$t=\frac{2\sqrt{6402319}}{33}-\frac{83}{3} t=-\frac{2\sqrt{6402319}}{33}-\frac{83}{3}$$

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

$$t=-\sqrt{\frac{2\sqrt{6402319}}{33}-\frac{83}{3}} t=\sqrt{\frac{2\sqrt{6402319}}{33}-\frac{83}{3}} t=-i\sqrt{\frac{2\sqrt{6402319}}{33}+\frac{83}{3}} t=i\sqrt{\frac{2\sqrt{6402319}}{33}+\frac{83}{3}}$$

Solve for t

$$t = -\frac{\sqrt{66 \sqrt{6402319} - 30129}}{33} \approx -11.21087248$$

$$t = \frac{\sqrt{66 \sqrt{6402319} - 30129}}{33} \approx 11.21087248$$

Steps Using the Quadratic Formula

Substitute t for t^{2}.

$$33t^{2}+1826t-750779=0$$

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 33 for a, 1826 for b, and -750779 for c in the quadratic formula.

$$t=\frac{-1826±\sqrt{1826^{2}-4\times 33\left(-750779\right)}}{2\times 33}$$

Do the calculations.

$$t=\frac{-1826±4\sqrt{6402319}}{66}$$

Solve the equation t=\frac{-1826±4\sqrt{6402319}}{66} when ± is plus and when ± is minus.

$$t=\frac{2\sqrt{6402319}}{33}-\frac{83}{3} t=-\frac{2\sqrt{6402319}}{33}-\frac{83}{3}$$

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

$$t=\sqrt{\frac{2\sqrt{6402319}}{33}-\frac{83}{3}} t=-\sqrt{\frac{2\sqrt{6402319}}{33}-\frac{83}{3}}$$