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The given equation is:

\[
x^2 - 14x + 49 = (x - a)^2
\]

We can solve for \(a\) by following these steps:

### Step 1: Simplify the right-hand side
Expand \((x - a)^2\):

\[
(x - a)^2 = x^2 - 2ax + a^2
\]

### Step 2: Set up the equation
Substitute this expansion back into the equation:

\[
x^2 - 14x + 49 = x^2 - 2ax + a^2
\]

### Step 3: Cancel out common terms
Since both sides have \(x^2\), we can subtract \(x^2\) from both sides:

\[
-14x + 49 = -2ax + a^2
\]

### Step 4: Compare coefficients
Now, compare the coefficients of \(x\) and the constants on both sides of the equation:
- For the \(x\)-terms: \(-14 = -2a\), which gives \(a = 7\).
- For the constants: \(49 = a^2\), and since \(a = 7\), this is consistent because \(7^2 = 49\).

### Final Answer:
The value of \(a\) is \( \boxed{7} \).

Would you like more details, or have any questions?

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Here are some related questions for further exploration:
1. How would the solution change if the coefficient of \(x\) in the original equation were different?
2. Can you generalize the steps used here to solve similar problems?
3. What is the significance of completing the square in solving quadratic equations?
4. How can you verify that \(a = 7\) is the correct solution?
5. How would the equation change if we expanded \((x - 7)^2\) and checked it directly?

**Tip**: Always try expanding both sides of the equation when solving for variables inside parentheses; it helps simplify the comparison!

Work out the value of a in the equation below: x^2 - 14x + 49 = (x - a)^2

Learn how to solve the quadratic equation x^2 - 14x + 49 = (x - a)^2 by expanding both sides and equating coefficients. This problem introduces key concepts like binomial expansion and quadratic equations, suitable for students in Grades 8-10.

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