Solve z^2-10z

$${ z }^{ 2 } -10z$$

Factor

$$z\left(z-10\right)$$

Solution Steps

Factor out z.

$$z\left(z-10\right)$$

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.

$$z^{2}-10z=0$$

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.

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

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

$$z=\frac{-\left(-10\right)±10}{2}$$

The opposite of -10 is 10.

$$z=\frac{10±10}{2}$$

Now solve the equation z=\frac{10±10}{2} when ± is plus. Add 10 to 10.

$$z=\frac{20}{2}$$

Divide 20 by 2.

$$z=10$$

Now solve the equation z=\frac{10±10}{2} when ± is minus. Subtract 10 from 10.

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

Divide 0 by 2.

$$z=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 10 for x_{1} and 0 for x_{2}.

$$z^{2}-10z=\left(z-10\right)z$$

Evaluate

$$z\left(z-10\right)$$