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If  (2x+5)(x-3)=14+7x-8, find the sum of the possible values of x.

 Apr 17, 2022
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Expand and move every term to one side.

\(\begin{array}{rcl} (2x + 5)(x - 3) &=& 14 + 7x -8\\ 2x^2 + 5x - 6x - 15 &=& 14 + 7x - 8\\ 2x^2 -8x-7&=&0 \end{array}\)

 

Let a and b be the possible values of x. Then by Vieta's formulae, \(a + b = 4\).

 

Therefore, the sum of possible values of x is 4.

 Apr 17, 2022

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