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].
Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]
The standard form of a quadratic equation is expressed as [tex]ax^2+bx+c=0[/tex]
Given the equation [tex]q^2+11q[/tex], we need to add a constant value that will make the expression a perfect square.
To complete the square, we will add the square of the half of the coefficient of q to the equation
Coefficient of q = 11
Half of the coefficient = 11/2
Square of the result = (11/2)² = 121/4
Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]
Learn more here: https://brainly.com/question/13981588
