SOLUTION: Find the constant p such that x^2 - 5x - 14x + x^2 + p is the square of a binomial.

Question 1209247: Find the constant p such that x^2 - 5x - 14x + x^2 + p is the square of a binomial.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Find the constant p such that x^2 - 5x - 14x + x^2 + p is the square of a binomial.
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Reduce to the standard form quadratic polynomial by combining like terms

    2x^2 - 19x + p.


Present it as a square of a binomial

    2x^2 - 19x + p = (ax+b)^2.


It is the same as

    2x^2 - 19x + p = a^2*x^2 + 2abx + b^2.


Hence,

    2   = a^2,  or  a = ;

    -19 = 2ab,  or  -19 = ,  which gives  b =  = ;

    p = b^2 =  = .

Solved.

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