Solve x=16/x

$$x = \frac { 16 } { x }$$

Solve for x

$$x=4$$

$$x=-4$$

Steps Using Difference of Squares

Subtract \frac{16}{x} from both sides.

$$x-\frac{16}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{16}{x}=0$$

Since \frac{xx}{x} and \frac{16}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-16}{x}=0$$

Do the multiplications in xx-16.

$$\frac{x^{2}-16}{x}=0$$

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

$$x^{2}-16=0$$

Consider x^{2}-16. Rewrite x^{2}-16 as x^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

To find equation solutions, solve x-4=0 and x+4=0.

$$x=4 x=-4$$

Steps by Finding Square Root

Subtract \frac{16}{x} from both sides.

$$x-\frac{16}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{16}{x}=0$$

Since \frac{xx}{x} and \frac{16}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-16}{x}=0$$

Do the multiplications in xx-16.

$$\frac{x^{2}-16}{x}=0$$

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

$$x^{2}-16=0$$

Add 16 to both sides. Anything plus zero gives itself.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Subtract \frac{16}{x} from both sides.

$$x-\frac{16}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{16}{x}=0$$

Since \frac{xx}{x} and \frac{16}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-16}{x}=0$$

Do the multiplications in xx-16.

$$\frac{x^{2}-16}{x}=0$$

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

$$x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$x=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$x=\frac{0±8}{2}$$

Now solve the equation x=\frac{0±8}{2} when ± is plus. Divide 8 by 2.

$$x=4$$

Now solve the equation x=\frac{0±8}{2} when ± is minus. Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$