How do you make $x^2 + 10x + c$ a perfect square?

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Answer 1 · 2015-04-10T13:04:20

Remember that the perfect square $(x+a)^2 = x^2+2ax+a^2$

So if $x^2+10x+c$ is a perfect square then
$2a = 0$
$rarr a=5$

and since $c=a^2$
$c=25$

How do you make x^2 + 10x + cx^2 + 10x + c a perfect square?