What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? 2x^2+42x+260=6x

Question

What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
2x^2+42x+260=6x
( )^2= ​

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Emery 2 weeks 2021-09-08T16:34:36+00:00 1 Answer 0

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    2021-09-08T16:36:08+00:00

    Equation 2x^{2} + 42x + 260 = 6x is in form of (x+9)^{2} = -49 . All the intermediate steps are shown above for the transformation .

    Step-by-step explanation:

    We have the following equation 2x^2+42x+260=6x or 2x^{2} + 42x + 260 = 6x . Let’s change this in form of (x+a)^2=b or (x+a)^{2} = b , following steps will be all intermediate steps involved :

    2x^{2} + 42x + 260 = 6x

    2x^{2} + 42x + 260 = 6x\\2(x^{2} + 21x+ 130) = 2(3x)\\(x^{2} + 21x+ 130)  = 3x\\x^{2}+18x+130 = 0

    x^{2} + 18x+130 = 0\\x^{2}+ 2(9)x+ 81 + 49 = 0\\x^{2}+ 2(9)x+ 81 = -49\\

    But, (x+9)^{2} = x^{2} + 18x+ 81   Therefore,

    (x+9)^{2} = -49

    So , equation 2x^{2} + 42x + 260 = 6x is in form of (x+9)^{2} = -49 . All the intermediate steps are shown above for the transformation .

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