Solve 1/50x(35000-x)=0

$$\frac { 1 } { 50 } x ( 35000 - x ) = 0$$

Solve for x

$$x=35000$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply \frac{1}{50}x by 35000-x.

$$\frac{1}{50}x\times 35000+\frac{1}{50}x\left(-1\right)x=0$$

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

$$\frac{1}{50}x\times 35000+\frac{1}{50}x^{2}\left(-1\right)=0$$

Multiply \frac{1}{50} and 35000 to get \frac{35000}{50}.

$$\frac{35000}{50}x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Divide 35000 by 50 to get 700.

$$700x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Multiply \frac{1}{50} and -1 to get -\frac{1}{50}.

$$700x-\frac{1}{50}x^{2}=0$$

Factor out x.

$$x\left(700-\frac{1}{50}x\right)=0$$

To find equation solutions, solve x=0 and 700-\frac{x}{50}=0.

$$x=0 x=35000$$

Steps Using the Quadratic Formula

Use the distributive property to multiply \frac{1}{50}x by 35000-x.

$$\frac{1}{50}x\times 35000+\frac{1}{50}x\left(-1\right)x=0$$

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

$$\frac{1}{50}x\times 35000+\frac{1}{50}x^{2}\left(-1\right)=0$$

Multiply \frac{1}{50} and 35000 to get \frac{35000}{50}.

$$\frac{35000}{50}x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Divide 35000 by 50 to get 700.

$$700x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Multiply \frac{1}{50} and -1 to get -\frac{1}{50}.

$$700x-\frac{1}{50}x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-\frac{1}{50}x^{2}+700x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{50} for a, 700 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-700±\sqrt{700^{2}}}{2\left(-\frac{1}{50}\right)}$$

Take the square root of 700^{2}.

$$x=\frac{-700±700}{2\left(-\frac{1}{50}\right)}$$

Multiply 2 times -\frac{1}{50}.

$$x=\frac{-700±700}{-\frac{1}{25}}$$

Now solve the equation x=\frac{-700±700}{-\frac{1}{25}} when ± is plus. Add -700 to 700.

$$x=\frac{0}{-\frac{1}{25}}$$

Divide 0 by -\frac{1}{25} by multiplying 0 by the reciprocal of -\frac{1}{25}.

$$x=0$$

Now solve the equation x=\frac{-700±700}{-\frac{1}{25}} when ± is minus. Subtract 700 from -700.

$$x=-\frac{1400}{-\frac{1}{25}}$$

Divide -1400 by -\frac{1}{25} by multiplying -1400 by the reciprocal of -\frac{1}{25}.

$$x=35000$$

The equation is now solved.

$$x=0 x=35000$$

Steps for Completing the Square

Use the distributive property to multiply \frac{1}{50}x by 35000-x.

$$\frac{1}{50}x\times 35000+\frac{1}{50}x\left(-1\right)x=0$$

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

$$\frac{1}{50}x\times 35000+\frac{1}{50}x^{2}\left(-1\right)=0$$

Multiply \frac{1}{50} and 35000 to get \frac{35000}{50}.

$$\frac{35000}{50}x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Divide 35000 by 50 to get 700.

$$700x+\frac{1}{50}x^{2}\left(-1\right)=0$$

Multiply \frac{1}{50} and -1 to get -\frac{1}{50}.

$$700x-\frac{1}{50}x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-\frac{1}{50}x^{2}+700x=0$$

Multiply both sides by -50.

$$\frac{-\frac{1}{50}x^{2}+700x}{-\frac{1}{50}}=\frac{0}{-\frac{1}{50}}$$

Dividing by -\frac{1}{50} undoes the multiplication by -\frac{1}{50}.

$$x^{2}+\frac{700}{-\frac{1}{50}}x=\frac{0}{-\frac{1}{50}}$$

Divide 700 by -\frac{1}{50} by multiplying 700 by the reciprocal of -\frac{1}{50}.

$$x^{2}-35000x=\frac{0}{-\frac{1}{50}}$$

Divide 0 by -\frac{1}{50} by multiplying 0 by the reciprocal of -\frac{1}{50}.

$$x^{2}-35000x=0$$

Divide -35000, the coefficient of the x term, by 2 to get -17500. Then add the square of -17500 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-35000x+\left(-17500\right)^{2}=\left(-17500\right)^{2}$$

Square -17500.

$$x^{2}-35000x+306250000=306250000$$

Factor x^{2}-35000x+306250000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-17500\right)^{2}=306250000$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-17500\right)^{2}}=\sqrt{306250000}$$

Simplify.

$$x-17500=17500 x-17500=-17500$$

Add 17500 to both sides of the equation.

$$x=35000 x=0$$