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Fill in the blank with a constant, so that the resulting quadratic is the square of a binomial.  x^2 + 4x + 5x +  ___

Feb 10, 2021

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We can complete the square. After simplifying, we get x^2 + 9x.

This simplifes to $$x^2 + 9x = (x + \frac{9}{2})^2 - \frac{81}{4}$$. So, the constant is 81/4.

Feb 20, 2021