Solve 0=x-x^2/50

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

Solve for x

$$x=50$$

$$x=0$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 50.

$$0=50x-x^{2}$$

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

$$50x-x^{2}=0$$

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.

$$-x^{2}+50x=0$$

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

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

Take the square root of 50^{2}.

$$x=\frac{-50±50}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-50±50}{-2}$$

Now solve the equation x=\frac{-50±50}{-2} when ± is plus. Add -50 to 50.

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

Divide 0 by -2.

$$x=0$$

Now solve the equation x=\frac{-50±50}{-2} when ± is minus. Subtract 50 from -50.

$$x=-\frac{100}{-2}$$

Divide -100 by -2.

$$x=50$$

The equation is now solved.

$$x=0 x=50$$

Steps for Completing the Square

Multiply both sides of the equation by 50.

$$0=50x-x^{2}$$

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

$$50x-x^{2}=0$$

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.

$$-x^{2}+50x=0$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide 50 by -1.

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

Divide 0 by -1.

$$x^{2}-50x=0$$

Divide -50, the coefficient of the x term, by 2 to get -25. Then add the square of -25 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-50x+\left(-25\right)^{2}=\left(-25\right)^{2}$$

Square -25.

$$x^{2}-50x+625=625$$

Factor x^{2}-50x+625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-25\right)^{2}=625$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{625}$$

Simplify.

$$x-25=25 x-25=-25$$

Add 25 to both sides of the equation.

$$x=50 x=0$$