Answer:[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]Step-by-step explanation:We have been given an expression [tex]q^2+11q[/tex]. We are asked to complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.We know that a perfect square trinomial is in form [tex]a^2+2ab+b^2[/tex].To convert our given expression into perfect square trinomial, we need to add and subtract [tex](\frac{b}{2})^2[/tex] from our given expression.We can see that value of b is 11, so we need to add and subtract [tex](\frac{11}{2})^2[/tex] to our expression as:[tex]q^2+11q+(\frac{11}{2})^2-(\frac{11}{2})^2[/tex]Upon comparing our expression with [tex](a+b)^2=a^2+2ab+b^2[/tex], we can see that [tex]a=q[/tex], [tex]2ab=11q[/tex] and [tex]b=\frac{11}{2}[/tex].Upon simplifying our expression, we will get:[tex](q+\frac{11}{2})^2-\frac{11^2}{2^2}[/tex][tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]Therefore, our perfect square would be [tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex].

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Answers #2

Answer:[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]Step-by-step explanation:The given expression is[tex]q^2+11q[/tex]We need to write the result as a binomial square.If an expression is [tex]x^2+bx[/tex], then we need to add [tex](\frac{b}{2})^2[/tex] in the expression to make it perfect square.In the given expression b=11 and x=q.[tex](\frac{b}{2})^2=(\frac{11}{2})^2[/tex]Add and subtract [tex](\frac{11}{2})^2[/tex] in the given expression.[tex]q^2+11q+(\frac{11}{2})^2-(\frac{11}{2})^2[/tex][tex](q+\frac{11}{2})^2-(\frac{11}{2})^2[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex][tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]Therefore, the result as a binomial square is [tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex].

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