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.

$(\frac{11}{2})^2$  

Let us simplify $(\frac{11}{2})^2$.

$\frac{11^2}{2^2}=\frac{121}{4}$

Upon adding $\frac{121}{4}$ on both sides, we will get:

$x^2 +11x+\frac{121}{4}=3+\frac{121}{4}$

Now we will make a common denominator for right side.

$x^2 +11x+\frac{121}{4}=\frac{12}{4}+\frac{121}{4}$

$x^2 +11x+\frac{121}{4}=\frac{133}{4}$

Therefore, our equation would be $x^2 +11x+\frac{121}{4}=\frac{133}{4}$.