Solve -x^2-9/(x^2-9)^2=0

$$\frac { - x ^ { 2 } - 9 } { ( x ^ { 2 } - 9 ) ^ { 2 } } = 0$$

Solve for x (complex solution)

$$x=-3i$$

$$x=3i$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)^{2}\left(x+3\right)^{2}.

$$-x^{2}-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$-x^{2}=9$$

Divide both sides by -1.

$$x^{2}=-9$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)^{2}\left(x+3\right)^{2}.

$$-x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-9\right)}}{2\left(-1\right)}$$

Multiply 4 times -9.

$$x=\frac{0±\sqrt{-36}}{2\left(-1\right)}$$

Take the square root of -36.

$$x=\frac{0±6i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±6i}{-2}$$

Now solve the equation x=\frac{0±6i}{-2} when ± is plus.

$$x=-3i$$

Now solve the equation x=\frac{0±6i}{-2} when ± is minus.

$$x=3i$$

The equation is now solved.

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