Solve 1/w=w+2/35

$$\frac { 1 } { w } = \frac { w + 2 } { 35 }$$

Solve for w

$$w=-7$$

$$w=5$$

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 35w, the least common multiple of w,35.

$$35=w\left(w+2\right)$$

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

$$35=w^{2}+2w$$

Swap sides so that all variable terms are on the left hand side.

$$w^{2}+2w=35$$

Subtract 35 from both sides.

$$w^{2}+2w-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-2±\sqrt{2^{2}-4\left(-35\right)}}{2}$$

Square 2.

$$w=\frac{-2±\sqrt{4-4\left(-35\right)}}{2}$$

Multiply -4 times -35.

$$w=\frac{-2±\sqrt{4+140}}{2}$$

Add 4 to 140.

$$w=\frac{-2±\sqrt{144}}{2}$$

Take the square root of 144.

$$w=\frac{-2±12}{2}$$

Now solve the equation w=\frac{-2±12}{2} when ± is plus. Add -2 to 12.

$$w=\frac{10}{2}$$

Divide 10 by 2.

$$w=5$$

Now solve the equation w=\frac{-2±12}{2} when ± is minus. Subtract 12 from -2.

$$w=-\frac{14}{2}$$

Divide -14 by 2.

$$w=-7$$

The equation is now solved.

$$w=5 w=-7$$

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 35w, the least common multiple of w,35.

$$35=w\left(w+2\right)$$

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

$$35=w^{2}+2w$$

Swap sides so that all variable terms are on the left hand side.

$$w^{2}+2w=35$$

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.

$$w^{2}+2w+1^{2}=35+1^{2}$$

Square 1.

$$w^{2}+2w+1=35+1$$

Add 35 to 1.

$$w^{2}+2w+1=36$$

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}.

$$\left(w+1\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w+1\right)^{2}}=\sqrt{36}$$

Simplify.

$$w+1=6 w+1=-6$$

Subtract 1 from both sides of the equation.

$$w=5 w=-7$$