Solve 0=x^4-6x^2+5

$$0 = x ^ { 4 } - 6 x ^ { 2 } + 5$$

Solve for x

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=\sqrt{5}\approx 2.236067977$$

$$x=1$$

$$x=-1$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{4}-6x^{2}+5=0$$

Substitute t for x^{2}.

$$t^{2}-6t+5=0$$

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, -6 for b, and 5 for c in the quadratic formula.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\times 5}}{2}$$

Do the calculations.

$$t=\frac{6±4}{2}$$

Solve the equation t=\frac{6±4}{2} when ± is plus and when ± is minus.

$$t=5 t=1$$

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

$$x=\sqrt{5} x=-\sqrt{5} x=1 x=-1$$