Solve x^4-7x^2+9=0

$$x ^ { 4 } - 7 x ^ { 2 } + 9 = 0$$

Solve for x

$$x=\frac{1-\sqrt{13}}{2}\approx -1.302775638$$

$$x = \frac{\sqrt{13} - 1}{2} \approx 1.302775638$$

$$x = \frac{\sqrt{13} + 1}{2} \approx 2.302775638$$

$$x=\frac{-\sqrt{13}-1}{2}\approx -2.302775638$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-7t+9=0$$

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, -7 for b, and 9 for c in the quadratic formula.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\times 9}}{2}$$

Do the calculations.

$$t=\frac{7±\sqrt{13}}{2}$$

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

$$t=\frac{\sqrt{13}+7}{2} t=\frac{7-\sqrt{13}}{2}$$

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

$$x=\frac{\sqrt{13}+1}{2} x=-\frac{\sqrt{13}+1}{2} x=-\frac{1-\sqrt{13}}{2} x=\frac{1-\sqrt{13}}{2}$$