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 What number goes in the box so that x^2 + ___x + 6x + 100 + 44 is the square of a binomial? If you find more than one, give your answer as a list.

 Apr 18, 2022
 #1
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x^2  +    __x + 100 + 44

 

x^2 +  ___x   + 144

 

Take  both square roots of  144   = 12   and  -12

 

Multiply both by 2  =   24   and  -24

 

Those are the  x^s  we need

 

Proof

 

(x - 12)^2  = x^2  - 24x  + 144

 

(x + 12)^2  = x^2 + 24x + 144

 

cool cool cool

 Apr 18, 2022

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