Solve x^4-12x^2+35=0

$$x ^ { 4 } - 12 x ^ { 2 } + 35 = 0$$

Solve for x

$$x=-\sqrt{7}\approx -2.645751311$$

$$x=\sqrt{7}\approx 2.645751311$$

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-12t+35=0$$

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, -12 for b, and 35 for c in the quadratic formula.

$$t=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 1\times 35}}{2}$$

Do the calculations.

$$t=\frac{12±2}{2}$$

Solve the equation t=\frac{12±2}{2} when ± is plus and when ± is minus.

$$t=7 t=5$$

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

$$x=\sqrt{7} x=-\sqrt{7} x=\sqrt{5} x=-\sqrt{5}$$