Question

Question #5db95

Answer 1

Complete the square, which will result in:

`x=0, x=16`

Explanation:

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`

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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]}