Finding a constant to make a perfect square trinomial

**geryuu** · September 13th 2009, 11:23 AM

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

x^2-15x

**e^(i*pi)** · September 13th 2009, 11:24 AM

Originally Posted by geryuu

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)

$(x+7.5)^2 + k = x^2 - 15x + 0$

$k = -(7.5^2)$

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More generally for $ax^2+bx = x^2 + \frac{b}{a}x$
(we can divide by a because it must be non-zero)

$(x+\frac{b}{2a})^2 - \frac{b^2}{4a^2}$

That second term in the fraction is the constant

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