Solve x^2=x*50

$$x ^ { 2 } = x \times 50$$

Solve for x

$$x=50$$

$$x=0$$

Steps Using Factoring

Subtract x\times 50 from both sides.

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

Multiply -1 and 50 to get -50.

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

Factor out x.

$$x\left(x-50\right)=0$$

To find equation solutions, solve x=0 and x-50=0.

$$x=0 x=50$$

Steps Using the Quadratic Formula

Subtract x\times 50 from both sides.

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

Multiply -1 and 50 to get -50.

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

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}.

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

Take the square root of \left(-50\right)^{2}.

$$x=\frac{-\left(-50\right)±50}{2}$$

The opposite of -50 is 50.

$$x=\frac{50±50}{2}$$

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

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

Divide 100 by 2.

$$x=50$$

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

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=50 x=0$$

Steps for Completing the Square

Subtract x\times 50 from both sides.

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

Multiply -1 and 50 to get -50.

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

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.

$$x=50 x=0$$