To complete the square for the equation [tex]\(x^2 - 10x = 7\)[/tex], follow these steps:
1. Identify the coefficient of [tex]\( x \)[/tex]: The coefficient of [tex]\( x \)[/tex] is [tex]\(-10\)[/tex].
2. Divide the coefficient of [tex]\( x \)[/tex] by 2:
This coefficient is [tex]\(-10\)[/tex]. When divided by 2, it gives [tex]\(-5\)[/tex].
3. Square the result from step 2:
Squaring [tex]\(-5\)[/tex] results in [tex]\( (-5)^2 = 25 \)[/tex].
Therefore, the number that should be added to both sides of the equation [tex]\(x^2 - 10x = 7\)[/tex] to complete the square is [tex]\(\boxed{25}\)[/tex].
