Solve x^4-10x^2=-16

$$x ^ { 4 } - 10 x ^ { 2 } = - 16$$

Solve for x

$$x=-2\sqrt{2}\approx -2.828427125$$

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Steps Using the Quadratic Formula

Add 16 to both sides.

$$x^{4}-10x^{2}+16=0$$

Substitute t for x^{2}.

$$t^{2}-10t+16=0$$

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 16 for c in the quadratic formula.

$$t=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 1\times 16}}{2}$$

Do the calculations.

$$t=\frac{10±6}{2}$$

Solve the equation t=\frac{10±6}{2} when ± is plus and when ± is minus.

$$t=8 t=2$$

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

$$x=2\sqrt{2} x=-2\sqrt{2} x=\sqrt{2} x=-\sqrt{2}$$