Solve -x*(x-8.1)=0

$$- x \cdot ( x - 8.1 ) = 0$$

Solve for x

$$x=8.1$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply -x by x-8.1.

$$\left(-x\right)x-8.1\left(-x\right)=0$$

Multiply -8.1 and -1 to get 8.1.

$$\left(-x\right)x+8.1x=0$$

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

$$-x^{2}+8.1x=0$$

Factor out x.

$$x\left(-x+8.1\right)=0$$

To find equation solutions, solve x=0 and -x+8.1=0.

$$x=0 x=\frac{81}{10}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -x by x-8.1.

$$\left(-x\right)x-8.1\left(-x\right)=0$$

Multiply -8.1 and -1 to get 8.1.

$$\left(-x\right)x+8.1x=0$$

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

$$-x^{2}+8.1x=0$$

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.

$$-x^{2}+\frac{81}{10}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, \frac{81}{10} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{81}{10}±\sqrt{\left(\frac{81}{10}\right)^{2}}}{2\left(-1\right)}$$

Take the square root of \left(\frac{81}{10}\right)^{2}.

$$x=\frac{-\frac{81}{10}±\frac{81}{10}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-\frac{81}{10}±\frac{81}{10}}{-2}$$

Now solve the equation x=\frac{-\frac{81}{10}±\frac{81}{10}}{-2} when ± is plus. Add -\frac{81}{10} to \frac{81}{10} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide 0 by -2.

$$x=0$$

Now solve the equation x=\frac{-\frac{81}{10}±\frac{81}{10}}{-2} when ± is minus. Subtract \frac{81}{10} from -\frac{81}{10} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{81}{5}}{-2}$$

Divide -\frac{81}{5} by -2.

$$x=\frac{81}{10}$$

The equation is now solved.

$$x=0 x=\frac{81}{10}$$

Steps for Completing the Square

Use the distributive property to multiply -x by x-8.1.

$$\left(-x\right)x-8.1\left(-x\right)=0$$

Multiply -8.1 and -1 to get 8.1.

$$\left(-x\right)x+8.1x=0$$

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

$$-x^{2}+8.1x=0$$

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.

$$-x^{2}+\frac{81}{10}x=0$$

Divide both sides by -1.

$$\frac{-x^{2}+\frac{81}{10}x}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\frac{\frac{81}{10}}{-1}x=\frac{0}{-1}$$

Divide \frac{81}{10} by -1.

$$x^{2}-\frac{81}{10}x=\frac{0}{-1}$$

Divide 0 by -1.

$$x^{2}-\frac{81}{10}x=0$$

Divide -\frac{81}{10}, the coefficient of the x term, by 2 to get -\frac{81}{20}. Then add the square of -\frac{81}{20} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{81}{10}x+\left(-\frac{81}{20}\right)^{2}=\left(-\frac{81}{20}\right)^{2}$$

Square -\frac{81}{20} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{81}{10}x+\frac{6561}{400}=\frac{6561}{400}$$

Factor x^{2}-\frac{81}{10}x+\frac{6561}{400}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{81}{20}\right)^{2}=\frac{6561}{400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{81}{20}\right)^{2}}=\sqrt{\frac{6561}{400}}$$

Simplify.

$$x-\frac{81}{20}=\frac{81}{20} x-\frac{81}{20}=-\frac{81}{20}$$

Add \frac{81}{20} to both sides of the equation.

$$x=\frac{81}{10} x=0$$