Solve 9n^4-46n^2+5=0

$$9 n ^ { 4 } - 46 n ^ { 2 } + 5 = 0$$

Solve for n

$$n=-\sqrt{5}\approx -2.236067977$$

$$n=\sqrt{5}\approx 2.236067977$$

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

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

Steps Using the Quadratic Formula

Substitute t for n^{2}.

$$9t^{2}-46t+5=0$$

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, -46 for b, and 5 for c in the quadratic formula.

$$t=\frac{-\left(-46\right)±\sqrt{\left(-46\right)^{2}-4\times 9\times 5}}{2\times 9}$$

Do the calculations.

$$t=\frac{46±44}{18}$$

Solve the equation t=\frac{46±44}{18} when ± is plus and when ± is minus.

$$t=5 t=\frac{1}{9}$$

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

$$n=\sqrt{5} n=-\sqrt{5} n=\frac{1}{3} n=-\frac{1}{3}$$