Solve x^4-65x^2+64=0

$$x ^ { 4 } - 65 x ^ { 2 } + 64 = 0$$

Solve for x

$$x=-8$$

$$x=8$$

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-65t+64=0$$

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, -65 for b, and 64 for c in the quadratic formula.

$$t=\frac{-\left(-65\right)±\sqrt{\left(-65\right)^{2}-4\times 1\times 64}}{2}$$

Do the calculations.

$$t=\frac{65±63}{2}$$

Solve the equation t=\frac{65±63}{2} when ± is plus and when ± is minus.

$$t=64 t=1$$

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

$$x=8 x=-8 x=1 x=-1$$