# Question #5db95

Sep 12, 2017

Complete the square, which will result in:

$x = 0 , x = 16$

#### Explanation:

To solve this problem, complete the square by adding ${\left(\setminus \frac{b}{2}\right)}^{2}$ to both sides of the equation:

${x}^{2} - 16 x = 0$

$\setminus \implies {x}^{2} - 16 x + {\left(\setminus \frac{- 16}{2}\right)}^{2} = {\left(\setminus \frac{- 16}{2}\right)}^{2}$

$\setminus \implies {x}^{2} - 16 x + 64 = 64$

Now the LHS is a perfect square, which means we can factor it into:

${\left(x - \setminus \frac{b}{2}\right)}^{2}$

$\setminus \implies {\left(x - 8\right)}^{2} = 64$

Taking the square root of both sides:

$\setminus \implies \setminus \sqrt{{\left(x - 8\right)}^{2}} = \setminus \sqrt{64}$

$\setminus \implies x - 8 = \setminus \pm 8$

$\setminus \implies x = 8 \setminus \pm 8$

$\setminus \therefore x = 0 , x = 16$

Those are the root, or zeros, of the quadratic equation.

If you want the parabola, it is:

graph{x^2-16 [-26.4, 24.94, -16.73, 8.93]}