To determine the number that should be added to both sides of the equation [tex]\( x^2 - 10x = 7 \)[/tex] to complete the square, follow these steps:
1. Identify the coefficient of the [tex]\( x \)[/tex] term: In the equation [tex]\( x^2 - 10x = 7 \)[/tex], the coefficient of [tex]\( x \)[/tex] is [tex]\(-10\)[/tex].
2. Divide this coefficient by 2:
[tex]\[
\frac{-10}{2} = -5
\][/tex]
3. Square the result from step 2:
[tex]\[
(-5)^2 = 25
\][/tex]
Hence, the number that should be added to both sides of the equation to complete the square is [tex]\( 25 \)[/tex].
This allows the left side of the equation [tex]\( x^2 - 10x + 25 \)[/tex] to be written in the form of a perfect square trinomial, making it [tex]\( (x - 5)^2 \)[/tex].
