Solve x^2(x^2-3)=4

$${ x }^{ 2 } ( { x }^{ 2 } -3)=4$$

Solve for x (complex solution)

$$x=2$$

$$x=-2$$

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x^{2} by x^{2}-3.

$$x^{4}-3x^{2}=4$$

Subtract 4 from both sides.

$$x^{4}-3x^{2}-4=0$$

Substitute t for x^{2}.

$$t^{2}-3t-4=0$$

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, -3 for b, and -4 for c in the quadratic formula.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 1\left(-4\right)}}{2}$$

Do the calculations.

$$t=\frac{3±5}{2}$$

Solve the equation t=\frac{3±5}{2} when ± is plus and when ± is minus.

$$t=4 t=-1$$

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

$$x=-2 x=2 x=-i x=i$$

Solve for x

$$x=-2$$

$$x=2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x^{2} by x^{2}-3.

$$x^{4}-3x^{2}=4$$

Subtract 4 from both sides.

$$x^{4}-3x^{2}-4=0$$

Substitute t for x^{2}.

$$t^{2}-3t-4=0$$

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, -3 for b, and -4 for c in the quadratic formula.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 1\left(-4\right)}}{2}$$

Do the calculations.

$$t=\frac{3±5}{2}$$

Solve the equation t=\frac{3±5}{2} when ± is plus and when ± is minus.

$$t=4 t=-1$$

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

$$x=2 x=-2$$