+964 Find all real values of $s$ such that $x^2 + sx + 144 - 63 + x^2 - 25 - 18$ is the square of a binomial.
+24 x^2 + sx + 144 - 63 + x^2 - 25 - 18
combine like terms:
2x^2 + sx + 38
if this is a square of a binomial then the first term must be (sqrt2 * x)
2x^2 + sx + 38 = (sqrt2 * x + [other term])^2
this other term has to be sqrt 38 because the contant term of the expression is 38
2x^2 + sx + 38 = (sqrt2 * x + sqrt38)^2
sx is 2ab according to binomial square expansion: (a+b)^2 = a^2 + 2ab + b^2
a = sqrt2 * x
b = sqrt38
so 2ab = sqrt76 * x
so s = sqrt76 = 2sqrt19
