Solve x^4-36x^2+35=0

$$x ^ { 4 } - 36 x ^ { 2 } + 35 = 0$$

Solve for x

$$x=-\sqrt{35}\approx -5.916079783$$

$$x=\sqrt{35}\approx 5.916079783$$

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-36t+35=0$$

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 1 for a, -36 for b, and 35 for c in the quadratic formula.

$$t=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 1\times 35}}{2}$$

Do the calculations.

$$t=\frac{36±34}{2}$$

Solve the equation t=\frac{36±34}{2} when ± is plus and when ± is minus.

$$t=35 t=1$$

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

$$x=\sqrt{35} x=-\sqrt{35} x=1 x=-1$$