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Answer 1 · 2017-09-12T22:23:14

Complete the square, which will result in:

#x=0, x=16#

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

#x^2-16x=0#

#\implies x^2-16x+(\frac{-16}{2})^2=(\frac{-16}{2})^2#

#\implies x^2-16x+64=64#

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

#(x-\frac{b}{2])^2#

#\implies (x-8)^2=64#

Taking the square root of both sides:

#\implies\sqrt{(x-8)^2}=\sqrt{64}#

#\implies x-8=\pm 8#

#\implies x=8\pm 8#

#\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]}