Question

Complete the square for the expression. Also, identify the resulting expression as a binomial squared.
x2 + 11x + ____

Answer 1

When completing the square is carried out on the quadratic $x^2+11x$ we get

$x^2+11x+\dfrac{121}{4}$

when expressed as a binomial squared, we get

$\left(x+\dfrac{11}{2}\right)^2$

To complete the square, we need to add a term to the expression

$x^2+11x$

that would make it a perfect square. Generally, given the quadratic expression

$x^2+bx$

to make it a perfect square, we have to add half the square of the coefficient of $x$. That is, add $\left(\frac{b}{2}\right)^2$, or $\frac{b^2}{4}$ to the quadratic expression to get

$x^2+bx+\dfrac{b^2}{4}$

which, when factored into a binomial squared becomes

$\left(x+\dfrac{b}{2}\right)^2$

In our case, the quadratic $x^2+11x$ will become

$x^2+11x+\dfrac{121}{4}$

and when expressed as a binomial squared, we get

$\left(x+\dfrac{11}{2}\right)^2$

Learn more about completing the square here https://brainly.com/question/2055939