SOLUTION: Please help me solve by completing the squares: {{{(x^2) - (6x) = (27)}}} {{{(2x^2) - (9x) + (9) = (0)}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve by completing the squares: {{{(x^2) - (6x) = (27)}}} {{{(2x^2) - (9x) + (9) = (0)}}}      Log On


   

Question 695644: Please help me solve by completing the squares:
%28x%5E2%29+-+%286x%29+=+%2827%29
%282x%5E2%29+-+%289x%29+%2B+%289%29+=+%280%29
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x^2) - (6x) = (27)
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x^2 - 6x + (6/2)^2 = 27 + (6/2)^2
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x^2 -6x + 9 = 27 + 9
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(x-3)^2 = 36
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x-3 = 6 or x - 3 = -3
x = 9 or x = 0
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(2x^2) - (9x) + (9) = (0)
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2[x^2 - (9/2)x + ?] = -9 + 2?
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2[x^2 -(9/2)x + (9/4)^2] = -9 + 2(9/4)^2
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2(x-(3/2))^2 = [-9*16 + 162]/16
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2(x-(3/2))^2 = 1/2
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(x-(3/2))^2 = 1/4
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x-(3/2) = 1/2 or x-(3/2) = -1/2
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x = 2 or x = 1
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Cheers,
Stan H.