Question

What number should be added to both sides of the equation to complete the squa
x2 - 10x = 7

Answer 1

Given:

The equation is:

`x^2-10x=7`

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
`x^2+bx`, then we have to add
`\left((b)/(2)\right)^2` to make it perfect square.

We have,

`x^2-10x=7` ...(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:

`\left((-10)/(2)\right)^2=(-5)^2`

`\left((-10)/(2)\right)^2=25`

On adding 25 on both sides of (i), we get

`x^2-10x+25=7+25`

`(x-5)^2=32`

Therefore, we need to add 25 to both sides of the equation to complete the square.