Solve x^4-14x^2+49=0

$$x ^ { 4 } - 14 x ^ { 2 } + 49 = 0$$

Solve for x

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-14t+49=0$$

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, -14 for b, and 49 for c in the quadratic formula.

$$t=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 1\times 49}}{2}$$

Do the calculations.

$$t=\frac{14±0}{2}$$

Solutions are the same.

$$t=7$$

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

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