Solve 36t^4+29t^2-7=0

$$36 t ^ { 4 } + 29 t ^ { 2 } - 7 = 0$$

Solve for t

$$t=-\frac{\sqrt{7}}{6}\approx -0.440958552$$

$$t=\frac{\sqrt{7}}{6}\approx 0.440958552$$

Steps Using the Quadratic Formula

Substitute t for t^{2}.

$$36t^{2}+29t-7=0$$

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, 29 for b, and -7 for c in the quadratic formula.

$$t=\frac{-29±\sqrt{29^{2}-4\times 36\left(-7\right)}}{2\times 36}$$

Do the calculations.

$$t=\frac{-29±43}{72}$$

Solve the equation t=\frac{-29±43}{72} when ± is plus and when ± is minus.

$$t=\frac{7}{36} t=-1$$

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

$$t=\frac{\sqrt{7}}{6} t=-\frac{\sqrt{7}}{6}$$