Solve 5x^4-12x^2+4=0

$$5 x ^ { 4 } - 12 x ^ { 2 } + 4 = 0$$

Solve for x

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

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

$$x=\frac{\sqrt{10}}{5}\approx 0.632455532$$

$$x=-\frac{\sqrt{10}}{5}\approx -0.632455532$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$5t^{2}-12t+4=0$$

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 5 for a, -12 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 5\times 4}}{2\times 5}$$

Do the calculations.

$$t=\frac{12±8}{10}$$

Solve the equation t=\frac{12±8}{10} when ± is plus and when ± is minus.

$$t=2 t=\frac{2}{5}$$

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

$$x=\sqrt{2} x=-\sqrt{2} x=\frac{\sqrt{10}}{5} x=-\frac{\sqrt{10}}{5}$$