Solve x^4-13x^2+30=0

$$x ^ { 4 } - 13 x ^ { 2 } + 30 = 0$$

Solve for x

$$x=-\sqrt{10}\approx -3.16227766$$

$$x=\sqrt{10}\approx 3.16227766$$

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-13t+30=0$$

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, -13 for b, and 30 for c in the quadratic formula.

$$t=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 1\times 30}}{2}$$

Do the calculations.

$$t=\frac{13±7}{2}$$

Solve the equation t=\frac{13±7}{2} when ± is plus and when ± is minus.

$$t=10 t=3$$

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

$$x=\sqrt{10} x=-\sqrt{10} x=\sqrt{3} x=-\sqrt{3}$$