Solve 36t^4+31t^2-5=0

$$36 t ^ { 4 } + 31 t ^ { 2 } - 5 = 0$$

Solve for t

$$t=-\frac{\sqrt{5}}{6}\approx -0.372677996$$

$$t=\frac{\sqrt{5}}{6}\approx 0.372677996$$

Steps Using the Quadratic Formula

Substitute t for t^{2}.

$$36t^{2}+31t-5=0$$

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 36 for a, 31 for b, and -5 for c in the quadratic formula.

$$t=\frac{-31±\sqrt{31^{2}-4\times 36\left(-5\right)}}{2\times 36}$$

Do the calculations.

$$t=\frac{-31±41}{72}$$

Solve the equation t=\frac{-31±41}{72} when ± is plus and when ± is minus.

$$t=\frac{5}{36} t=-1$$

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

$$t=\frac{\sqrt{5}}{6} t=-\frac{\sqrt{5}}{6}$$