Question
Fill in the blank with a number to make the expression a perfeçt square,
Ask by Alexander Carrillo. in the United States
Feb 08,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To make the expression a perfect square, add 25.
Solution
It looks like some details are missing. Could you please provide the complete expression or more context? For example, if you have a quadratic such as
x² + 10x + _____
then to “complete the square” you would add (10⁄2)² = 25 so that
x² + 10x + 25 = (x + 5)²
If you can share the full expression you’re working with, I’d be happy to help further!
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To create a perfect square from an expression, the goal is often to have the form \( (a + b)^2 \) or \( (a - b)^2 \). For example, if you have an expression like \( x^2 + 6x + \_\_\_ \), you would want to fill in the blank with \( 9 \) to make it \( (x + 3)^2 \). The key is to take half of the coefficient of \( x \) (which is \( 6 \)), square it (yielding \( 9 \)), and then add it to complete the square. Alternatively, if you have a quadratic like \( x^2 - 4x + \_\_\_ \), adding \( 4 \) (which is \( (2)^2 \)) will also yield \( (x - 2)^2 \). Finding that magic number involves a bit of simplifying, but it can be a fun challenge!
