Solve 4x^4+91x^2-225=0

$$4 { x }^{ 4 } +91 { x }^{ 2 } -225=0$$

Solve for x (complex solution)

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$x=-5i$$

$$x=5i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$4t^{2}+91t-225=0$$

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 4 for a, 91 for b, and -225 for c in the quadratic formula.

$$t=\frac{-91±\sqrt{91^{2}-4\times 4\left(-225\right)}}{2\times 4}$$

Do the calculations.

$$t=\frac{-91±109}{8}$$

Solve the equation t=\frac{-91±109}{8} when ± is plus and when ± is minus.

$$t=\frac{9}{4} t=-25$$

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

$$x=-\frac{3}{2} x=\frac{3}{2} x=-5i x=5i$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$4t^{2}+91t-225=0$$

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 4 for a, 91 for b, and -225 for c in the quadratic formula.

$$t=\frac{-91±\sqrt{91^{2}-4\times 4\left(-225\right)}}{2\times 4}$$

Do the calculations.

$$t=\frac{-91±109}{8}$$

Solve the equation t=\frac{-91±109}{8} when ± is plus and when ± is minus.

$$t=\frac{9}{4} t=-25$$

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

$$x=\frac{3}{2} x=-\frac{3}{2}$$