find a constant to add to the binomial so that it becomes a perfect square trinomial.
x^2-15x
Divide the coefficient of the linear term by 2 (ie divide b by 2)
$\displaystyle (x+7.5)^2 + k = x^2 - 15x + 0$
$\displaystyle k = -(7.5^2)$
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More generally for $\displaystyle ax^2+bx = x^2 + \frac{b}{a}x$
(we can divide by a because it must be non-zero)
$\displaystyle (x+\frac{b}{2a})^2 - \frac{b^2}{4a^2}$
That second term in the fraction is the constant