Solve x^4-10x^2+9=0

$$x ^ { 4 } - 10 x ^ { 2 } + 9 = 0$$

Solve for x

$$x=-3$$

$$x=3$$

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-10t+9=0$$

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, -10 for b, and 9 for c in the quadratic formula.

$$t=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 1\times 9}}{2}$$

Do the calculations.

$$t=\frac{10±8}{2}$$

Solve the equation t=\frac{10±8}{2} when ± is plus and when ± is minus.

$$t=9 t=1$$

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

$$x=3 x=-3 x=1 x=-1$$