Find the value of c that makes the trinomial a perfect square.

 

x2+26x+c

To make the trinomial \( x^2 + 26x + c \) a perfect square, we need to complete the square.

The standard form of a perfect square trinomial is:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

For the given trinomial \( x^2 + 26x + c \), we can compare it to \( (x + b)^2 = x^2 + 2bx + b^2 \). Here, \( 2b = 26 \), so:

\[
b = \frac{26}{2} = 13
\]

Now, to find \( c \), we square \( b \):

\[
c = b^2 = 13^2 = 169
\]

Thus, the value of \( c \) that makes the trinomial a perfect square is:

\[
c = 169
\]

### Do you want further details or have any questions? 

Here are 5 related questions:
1. How would you factor \( x^2 + 26x + 169 \)?
2. What is the general process for completing the square?
3. Can you find the value of \( c \) for other trinomials, like \( x^2 + 10x + c \)?
4. What is the importance of perfect square trinomials in solving quadratic equations?
5. How does completing the square relate to the quadratic formula?

**Tip:** To complete the square, always take half of the middle term's coefficient and square it.

Find the value of c that makes the trinomial a perfect square. x^2 + 26x + c

Discover how to find the value of c that turns the trinomial x^2 + 26x + c into a perfect square using the method of completing the square. This solution involves key algebraic concepts like perfect square trinomials and is suitable for students in Grades 8-10.

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