Question

Which of the following statements is not true about completing the square? Completing the square will always work.

Completing the square changes the value of the equation.
When completing the square you add and subtract the same value to the equation. When completing the square you create a perfect square binomial.

Answer 1

Completing the square changes the value of the equation.

Explanation:

FALSE

Answer 2

Answer: Completing the square changes the value of the equation.

Explanation:

For example we have expression :
`x^2+ax`

which is equivalent to
`x^2+2(a)/(2)x`

We add and subtract
`((a)/(2))^2` to form a complete square.

`x^2+ax+((a)/(2))^2-((a)/(2))^2`

`=(x+(a)/(2))^2-((a)/(2))^2`, where
`(x+(a)/(2))^2` is a perfect square binomial.

Thus, the true statements about the completing squares are:-

• Completing the square will always work.
• When completing the square you add and subtract the same value to the equation.
• When completing the square you create a perfect square binomial.

Completing the square does not change the value of the equation.