Solve 0=0.1x^4-2x^2+6.4

$$0 = 0.1 x ^ { 4 } - 2 x ^ { 2 } + 6.4$$

Solve for x

$$x=-4$$

$$x=4$$

$$x=2$$

$$x=-2$$

Steps Using the Quadratic Formula

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

$$0.1x^{4}-2x^{2}+6.4=0$$

Substitute t for x^{2}.

$$0.1t^{2}-2t+6.4=0$$

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 0.1 for a, -2 for b, and 6.4 for c in the quadratic formula.

$$t=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 0.1\times 6.4}}{0.1\times 2}$$

Do the calculations.

$$t=\frac{2±\frac{6}{5}}{0.2}$$

Solve the equation t=\frac{2±\frac{6}{5}}{0.2} when ± is plus and when ± is minus.

$$t=16 t=4$$

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

$$x=4 x=-4 x=2 x=-2$$