find a constant to add to the binomial so that it becomes a perfect square trinomial.

x^2-15x

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- Sep 13th 2009, 11:23 AMgeryuuFinding a constant to make a perfect square trinomial
find a constant to add to the binomial so that it becomes a perfect square trinomial.

x^2-15x - Sep 13th 2009, 11:24 AMe^(i*pi)
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