Solve 36x^4=85x^2-49

$$36 x ^ { 4 } = 85 x ^ { 2 } - 49$$

Solve for x

$$x = -\frac{7}{6} = -1\frac{1}{6} \approx -1.166666667$$

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Subtract 85x^{2} from both sides.

$$36x^{4}-85x^{2}=-49$$

Add 49 to both sides.

$$36x^{4}-85x^{2}+49=0$$

Substitute t for x^{2}.

$$36t^{2}-85t+49=0$$

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, -85 for b, and 49 for c in the quadratic formula.

$$t=\frac{-\left(-85\right)±\sqrt{\left(-85\right)^{2}-4\times 36\times 49}}{2\times 36}$$

Do the calculations.

$$t=\frac{85±13}{72}$$

Solve the equation t=\frac{85±13}{72} when ± is plus and when ± is minus.

$$t=\frac{49}{36} t=1$$

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

$$x=\frac{7}{6} x=-\frac{7}{6} x=1 x=-1$$