Solve w/10-w+5/5w=-1/w

$$\frac { w } { 10 } - \frac { w + 5 } { 5 w } = - \frac { 1 } { w }$$

Solve for w

$$w=2$$

Steps Using the Quadratic Formula

Variable w cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10w, the least common multiple of 10,5w,w.

$$ww-2\left(w+5\right)=-10$$

Multiply w and w to get w^{2}.

$$w^{2}-2\left(w+5\right)=-10$$

Use the distributive property to multiply -2 by w+5.

$$w^{2}-2w-10=-10$$

Add 10 to both sides.

$$w^{2}-2w-10+10=0$$

Add -10 and 10 to get 0.

$$w^{2}-2w=0$$

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

$$w=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}}}{2}$$

Take the square root of \left(-2\right)^{2}.

$$w=\frac{-\left(-2\right)±2}{2}$$

The opposite of -2 is 2.

$$w=\frac{2±2}{2}$$

Now solve the equation w=\frac{2±2}{2} when ± is plus. Add 2 to 2.

$$w=\frac{4}{2}$$

Divide 4 by 2.

$$w=2$$

Now solve the equation w=\frac{2±2}{2} when ± is minus. Subtract 2 from 2.

$$w=\frac{0}{2}$$

Divide 0 by 2.

$$w=0$$

The equation is now solved.

$$w=2 w=0$$

Variable w cannot be equal to 0.

$$w=2$$

Steps for Completing the Square

Variable w cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10w, the least common multiple of 10,5w,w.

$$ww-2\left(w+5\right)=-10$$

Multiply w and w to get w^{2}.

$$w^{2}-2\left(w+5\right)=-10$$

Use the distributive property to multiply -2 by w+5.

$$w^{2}-2w-10=-10$$

Add 10 to both sides.

$$w^{2}-2w=-10+10$$

Add -10 and 10 to get 0.

$$w^{2}-2w=0$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}-2w+1=1$$

Factor w^{2}-2w+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(w-1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$w-1=1 w-1=-1$$

Add 1 to both sides of the equation.

$$w=2 w=0$$

Variable w cannot be equal to 0.

$$w=2$$