Answer: Completing the square changes the value of the equation.
Step-by-step explanation:
For example we have expression : [tex]x^2+ax[/tex]
which is equivalent to [tex]x^2+2\frac{a}{2}x[/tex]
We add and subtract [tex](\frac{a}{2})^2[/tex] to form a complete square.
[tex]x^2+ax+(\frac{a}{2})^2-(\frac{a}{2})^2[/tex]
[tex]=(x+\frac{a}{2})^2-(\frac{a}{2})^2[/tex], where [tex](x+\frac{a}{2})^2[/tex] 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.
