Solve -5x^-4=5/x^6

$$- 5 x ^ { - 4 } = \frac { 5 } { x ^ { 6 } }$$

Solve for x (complex solution)

$$x=i$$

$$x=-i$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{6}.

$$-5x^{-4}x^{6}=5$$

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$-5x^{2}=5$$

Divide both sides by -5.

$$x^{2}=\frac{5}{-5}$$

Divide 5 by -5 to get -1.

$$x^{2}=-1$$

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{6}.

$$-5x^{-4}x^{6}=5$$

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$-5x^{2}=5$$

Subtract 5 from both sides.

$$-5x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\left(-5\right)}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\left(-5\right)}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\left(-5\right)}}{2\left(-5\right)}$$

Multiply 20 times -5.

$$x=\frac{0±\sqrt{-100}}{2\left(-5\right)}$$

Take the square root of -100.

$$x=\frac{0±10i}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±10i}{-10}$$

Now solve the equation x=\frac{0±10i}{-10} when ± is plus.

$$x=-i$$

Now solve the equation x=\frac{0±10i}{-10} when ± is minus.

$$x=i$$

The equation is now solved.

$$x=-i x=i$$