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

 x^2+ 26x + c

To make the expression \( x^2 + 26x + c \) a perfect square trinomial, we use the method of completing the square.

1. Start with the linear term \( 26x \). Take half of the coefficient of \( x \), which is \( 26 \), and divide it by 2:

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

2. Then, square this value:

\[
13^2 = 169
\]

Thus, \( c = 169 \).

Therefore, the value of \( c \) that makes \( x^2 + 26x + c \) a perfect square trinomial is \( \boxed{169} \).

Would you like further details on completing the square or any other clarifications?

Here are 5 related questions for practice:
1. What is the perfect square trinomial for \( x^2 + 14x + c \)?
2. How do you factor the trinomial \( x^2 + 26x + 169 \)?
3. What is the general formula for completing the square of any quadratic expression \( ax^2 + bx + c \)?
4. Can the expression \( x^2 + 26x - c \) ever be a perfect square trinomial?
5. How would you solve the equation \( x^2 + 26x + 169 = 0 \)?

**Tip:** When completing the square, always remember to halve the coefficient of the linear term and then square it to find the constant.

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

Learn how to find the value of c that makes x^2 + 26x + c a perfect square trinomial. This detailed explanation walks through completing the square and key algebraic steps. Ideal for students in Grades 8-10.

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