Which of the following statements is true?

A.
Any quadratic equation can be solved by completing the square.
B.
Completing the square always gives two distinct solutions.
C.
You can’t complete the square if there is no constant in the equation.
D.
You can only use completing the square when the x-term in the equation is even.

I betcha I can solve any quadratic equation by completing the square.

But isn't it also true that you can't complete the square if there is no constant?

e.g.

x^2 - 6x = 0
add 9 to both sides
x^2 - 6x + 9 = 9
(x-3)^2 = 9
x-3 = ±3
x = 3 ± 3 = 6 or 0

check:
by factoring,
x(x-6) = 0
x = 0 or x = 6 , as above

Which of the following statements is not true about completing the square?

To determine which statement is true, let's analyze each one:

A. "Any quadratic equation can be solved by completing the square."
To verify this statement, we can use the general form of a quadratic equation: ax^2 + bx + c = 0. Completing the square is a method that can be applied to any quadratic equation, so statement A is true.

B. "Completing the square always gives two distinct solutions."
Completing the square can result in two distinct solutions, but it can also lead to a single solution or no real solutions, depending on the quadratic equation. Therefore, statement B is false.

C. "You can't complete the square if there is no constant in the equation."
Completing the square can still be applied if the quadratic equation does not have a constant term. In this case, c would be zero, but the method can still be used. So, statement C is false.

D. "You can only use completing the square when the x-term in the equation is even."
This statement is false as well. The method of completing the square can be used regardless of whether the coefficient of the x-term is even or odd.

In summary, statement A is true, while statements B, C, and D are false.