What value of 𝑐*c*​ will complete the square in the expression below to make it a perfect square trinomial?

𝑥2−13𝑥+𝑐*x*2−13*x*+*c*

𝑐=*c*=

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Enter the perfect square trinomial as a squared binomial.

To complete the square for the expression \( x^2 - 13x + c \), we need to find the value of \( c \) that will make the expression a perfect square trinomial.

### Step 1: Identify the coefficient of the linear term
The coefficient of the linear term (the term with \( x \)) is \(-13\).

### Step 2: Divide the coefficient by 2
\[
\text{Half of } -13 \text{ is } \frac{-13}{2} = -\frac{13}{2}.
\]

### Step 3: Square the result
\[
\left(-\frac{13}{2}\right)^2 = \frac{169}{4}.
\]

### Step 4: Substitute this value for \( c \)
The value of \( c \) that completes the square is \( \frac{169}{4} \).

### Step 5: Write the expression as a perfect square trinomial
Now, the expression can be written as:
\[
x^2 - 13x + \frac{169}{4} = \left(x - \frac{13}{2}\right)^2.
\]

### Final Answer:
\[
c = \frac{169}{4}.
\]
The perfect square trinomial is \( \left(x - \frac{13}{2}\right)^2 \).

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would you complete the square for the expression \( x^2 + 6x + c \)?
2. What are the steps to solve a quadratic equation using the method of completing the square?
3. How can completing the square be used to derive the quadratic formula?
4. How does completing the square help in solving quadratic equations that cannot be factored easily?
5. What is the geometric interpretation of completing the square?

**Tip:** Completing the square is a valuable technique for rewriting quadratic equations in a form that makes them easier to solve or graph.

Learn how to complete the square for the quadratic expression x^2 - 13x + c to make it a perfect square trinomial. Find out the value of c that completes the square and understand the steps involved. Suitable for advanced high school students and those preparing for standardized tests.

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