Solve x^2-21x

$$x ^ { 2 } - 21 x$$

Factor

$$x\left(x-21\right)$$

Solution Steps

Factor out x.

$$x\left(x-21\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$x^{2}-21x=0$$

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.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}}}{2}$$

Take the square root of \left(-21\right)^{2}.

$$x=\frac{-\left(-21\right)±21}{2}$$

The opposite of -21 is 21.

$$x=\frac{21±21}{2}$$

Now solve the equation x=\frac{21±21}{2} when ± is plus. Add 21 to 21.

$$x=\frac{42}{2}$$

Divide 42 by 2.

$$x=21$$

Now solve the equation x=\frac{21±21}{2} when ± is minus. Subtract 21 from 21.

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

Divide 0 by 2.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 21 for x_{1} and 0 for x_{2}.

$$x^{2}-21x=\left(x-21\right)x$$

Evaluate

$$x\left(x-21\right)$$