what value of c makes x to the second power minus 12x plus c a perfect square trinomial 

To make the quadratic expression \( x^2 - 12x + c \) a perfect square trinomial, the constant \( c \) must complete the square. 

The general form of a perfect square trinomial is \( (x - a)^2 = x^2 - 2ax + a^2 \). Comparing this with your expression \( x^2 - 12x + c \), we can see that \( -12x \) corresponds to \( -2ax \). Therefore:

\[
-2a = -12 \quad \Rightarrow \quad a = 6
\]

To complete the square, \( c \) should be equal to \( a^2 \), so:

\[
c = 6^2 = 36
\]

Thus, the value of \( c \) that makes \( x^2 - 12x + c \) a perfect square trinomial is \( 36 \).

The expression becomes:
\[
x^2 - 12x + 36 = (x - 6)^2
\]

Would you like more details or have any further questions?

Here are 5 related questions to explore further:
1. How do you complete the square for a quadratic expression?
2. What is the vertex form of a quadratic equation?
3. How does completing the square help in solving quadratic equations?
4. How can you determine if a quadratic trinomial is already a perfect square?
5. What is the significance of the discriminant in quadratic equations?

**Tip**: Completing the square is useful in many areas of algebra, including solving quadratic equations and deriving the quadratic formula!

What value of c makes x to the second power minus 12x plus c a perfect square trinomial?

Discover how to determine the value of c that makes the quadratic expression x^2 - 12x + c a perfect square trinomial. This step-by-step solution explains completing the square, using the formula c = (b/2)^2. Ideal for students in Grades 8-10 learning algebraic concepts.

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