Solve (x-0,3)x=0

$$( x - 0,3 ) x = 0$$

Solve for x

$$x=0$$

$$x=0,3$$

Steps Using Factoring

Use the distributive property to multiply x-0,3 by x.

$$x^{2}-0,3x=0$$

Factor out x.

$$x\left(x-0,3\right)=0$$

To find equation solutions, solve x=0 and x-0,3=0.

$$x=0 x=\frac{3}{10}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-0,3 by x.

$$x^{2}-0,3x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -0,3 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-0,3\right)±\sqrt{\left(-0,3\right)^{2}}}{2}$$

Take the square root of \left(-0,3\right)^{2}.

$$x=\frac{-\left(-0,3\right)±\frac{3}{10}}{2}$$

The opposite of -0,3 is 0,3.

$$x=\frac{0,3±\frac{3}{10}}{2}$$

Now solve the equation x=\frac{0,3±\frac{3}{10}}{2} when ± is plus. Add 0,3 to \frac{3}{10} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{3}{5}}{2}$$

Divide \frac{3}{5} by 2.

$$x=\frac{3}{10}$$

Now solve the equation x=\frac{0,3±\frac{3}{10}}{2} when ± is minus. Subtract \frac{3}{10} from 0,3 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=\frac{3}{10} x=0$$

Steps for Completing the Square

Use the distributive property to multiply x-0,3 by x.

$$x^{2}-0,3x=0$$

Divide -0,3, the coefficient of the x term, by 2 to get -0,15. Then add the square of -0,15 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-0,3x+\left(-0,15\right)^{2}=\left(-0,15\right)^{2}$$

Square -0,15 by squaring both the numerator and the denominator of the fraction.

$$x^{2}-0,3x+0,0225=0,0225$$

Factor x^{2}-0,3x+0,0225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-0,15\right)^{2}=0,0225$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-0,15\right)^{2}}=\sqrt{0,0225}$$

Simplify.

$$x-0,15=\frac{3}{20} x-0,15=-\frac{3}{20}$$

Add 0,15 to both sides of the equation.

$$x=\frac{3}{10} x=0$$