Solve x^4+34x^2+225=0

$$x ^ { 4 } + 34 x ^ { 2 } + 225 = 0$$

Solve for x (complex solution)

$$x=3i$$

$$x=-3i$$

$$x=-5i$$

$$x=5i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+34t+225=0$$

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, 34 for b, and 225 for c in the quadratic formula.

$$t=\frac{-34±\sqrt{34^{2}-4\times 1\times 225}}{2}$$

Do the calculations.

$$t=\frac{-34±16}{2}$$

Solve the equation t=\frac{-34±16}{2} when ± is plus and when ± is minus.

$$t=-9 t=-25$$

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

$$x=-3i x=3i x=-5i x=5i$$