[tex]\boxed{c=11}[/tex]
Explanation:
Here we have the following expression:
[tex]x^2+22x+c[/tex]
A Perfect Square Trinomial is given by the form:
[tex](x+a)^2=x^2+2ax+a^2[/tex]
So matching terms, we can conclude that:
[tex]2a=22 \\ \\ a=11 \\ \\ c=a^2=121[/tex]
So, substituting c into the expression:
[tex]x^2+22x+121[/tex]
It is a perfect square because:
[tex]x^2+22x+121=(x+11)^2[/tex]
Learn more:
Quadratic Equation in real life problems: https://brainly.com/question/10278062
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