Question

What constant term should be added to both sides to complete the square on the left side? x 2 - x + _____ = 10

Answer 1

To complete the square, add 1/4 to both sides of the equation.

Step-by-step explanation:

To complete the square on the left side of the equation x² - x + _____ = 10, we need to take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x is -1, so half of it is -1/2. Squaring -1/2 gives us 1/4. Therefore, we need to add 1/4 to both sides of the equation.

Adding 1/4 to both sides of the equation gives us x² - x + 1/4 = 10 + 1/4.

The equation after completing the square is x² - x + 1/4 = 41/4.

Answer 2

The required term is
`((1)/(2))^2`

Step-by-step explanation:

Given : Equation
`x^2-x+.....=10`

To find : What constant term should be added to both sides to complete the square on the left side?

Solution :

The quadratic equation is in the form
`ax^2+bx+c=0`

To complete the square we have to add the term
`((b)/(2))^2`

If we compare the equation, b=-1

So, The term has to add is
`((-1)/(2))^2=((1)/(2))^2`

Substitute the term in the equation as adding it on both side,

`x^2-x+((1)/(2))^2=10+((1)/(2))^2`

Now, we solve to make a complete square,

`(x-(1)/(2))^2=10+(1)/(4)`

`(x-(1)/(2))^2=(41)/(4)`

Therefore, The required term is
`((1)/(2))^2`