Question

Let x^2 +11x=3 ​.

What values make an equivalent number sentence after completing the square?

Enter your answers between the parentheses.
x^2 +11x+( )=( )

Answer 1

The answer is x^2+11x+(121/4)=(143/4)

Answer 2

We have been given an equation
`x^2 +11x=3`. We are asked to complete the square for the given equation.

To complete the square for our given equation, we need to add the half the square of x term on both sides.

We can see that coefficient of x term is 11, so we need to add half the square of 11 on both sides.

`((11)/(2))^2`

Let us simplify
`((11)/(2))^2`.

`(11^2)/(2^2)=(121)/(4)`

Upon adding
`(121)/(4)` on both sides, we will get:

`x^2 +11x+(121)/(4)=3+(121)/(4)`

Now we will make a common denominator for right side.

`x^2 +11x+(121)/(4)=(12)/(4)+(121)/(4)`

`x^2 +11x+(121)/(4)=(133)/(4)`

Therefore, our equation would be
`x^2 +11x+(121)/(4)=(133)/(4)`.