Solve 9x^4-10x^2+1=0

$$9 x ^ { 4 } - 10 x ^ { 2 } + 1 = 0$$

Solve for x

$$x=-1$$

$$x=1$$

$$x=\frac{1}{3}\approx 0.333333333$$

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$9t^{2}-10t+1=0$$

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 9 for a, -10 for b, and 1 for c in the quadratic formula.

$$t=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 9\times 1}}{2\times 9}$$

Do the calculations.

$$t=\frac{10±8}{18}$$

Solve the equation t=\frac{10±8}{18} when ± is plus and when ± is minus.

$$t=1 t=\frac{1}{9}$$

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

$$x=1 x=-1 x=\frac{1}{3} x=-\frac{1}{3}$$