Complete the Perfect Square: Solve (x-?)² = x²-?+25

Fill in the blanks:

$(x-?)^2=x^2-?+25$

To solve this problem, we'll follow these steps:

• Step 1: Recognize this as a binomial square problem.
• Step 2: Identify the expanded form of a binomial square.
• Step 3: Match the terms from both sides of the equation.

Now, let's work through each step:
Step 1: The given expression $(x-?)^2 = x^2 - ? + 25$ is the expansion of a binomial $(x-a)^2$.
Step 2: Recall that $(x-a)^2 = x^2 - 2ax + a^2$.
Step 3: Compare this equivalent form to $x^2 - ? + 25$:

- The term $x^2$ matches directly on both sides.
- The constant term $a^2 = 25$, so $a = 5$ because $5^2 = 25$.
- The middle term $-2ax$ is currently unspecified, but it provides the form needed to fill the blank with $-2ax$.

Matching the expanded form: - The term inside $(x-?)$ should be $5$ (because $a=5$).
- Therefore, the missing linear term can be $10x$ since $-2 \times 5 = -10$.

Therefore, the solution to the problem is $5,\text{ }10x$.