Solve x^4-58x^2+441=0

$$x ^ { 4 } - 58 x ^ { 2 } + 441 = 0$$

Solve for x

$$x=-7$$

$$x=7$$

$$x=3$$

$$x=-3$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-58t+441=0$$

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, -58 for b, and 441 for c in the quadratic formula.

$$t=\frac{-\left(-58\right)±\sqrt{\left(-58\right)^{2}-4\times 1\times 441}}{2}$$

Do the calculations.

$$t=\frac{58±40}{2}$$

Solve the equation t=\frac{58±40}{2} when ± is plus and when ± is minus.

$$t=49 t=9$$

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

$$x=7 x=-7 x=3 x=-3$$