Respuesta :
Given:
The equation is:
[tex]x^2-10x=7[/tex]
To find:
The number that should be added to sides of the equation to complete the square.
Solution:
If an expression is in the form of [tex]x^2+bx[/tex], then we have to add [tex]\left(\dfrac{b}{2}\right)^2[/tex] to make it perfect square.
We have,
[tex]x^2-10x=7[/tex] ...(i)
To make it perfect square we need to add square of half of coefficient of x on both sides.
Coefficient of x is -10, so square of half of coefficient of x is:
[tex]\left(\dfrac{-10}{2}\right)^2=(-5)^2[/tex]
[tex]\left(\dfrac{-10}{2}\right)^2=25[/tex]
On adding 25 on both sides of (i), we get
[tex]x^2-10x+25=7+25[/tex]
[tex](x-5)^2=32[/tex]
Therefore, we need to add 25 to both sides of the equation to complete the square.
