Question

Which of the following statements is true about completing a square? A. When completing the square, subtract the square of half the coefficient of x from both sides of the equation. B. When completing the square, add the square of half the coefficient of x to only the x^2+bx side of the equation. C. When completing the square, add half the coefficient of x to both sides of the equation. D. When completing the square, add the square of half the coefficient of x to both sides of the equation.

Answer 1

D

Explanation:

So, let's say that we have the following equation:

`x^2+bx=0`

And we want to complete the square.

What we need to do is to divide the coefficient of x by half. Square that. Then add that number to both sides.

The answer that reflects this is choice D.

For instance if we have:

`x^2+4x=0`

Divide 4 by 2 and then square it.

4/2 is 2. 2²=4. Add 4 to both sides. Thus:

`(x^2+4x)+4=0+4`

And now, we can complete the square:

`(x+2)^2=4`