SOLUTION: (x+3)-2(x+4)=(x-4)(x-3)

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Question 65412: (x+3)-2(x+4)=(x-4)(x-3)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
(x+3) - 2(x+4) = (x-4)(x-3)

Put a 1 before the first parenthesis on the left

1(x+3) - 2(x+4) = (x-4)(x-3)

Remove parentheses on left by distributing.
Use FOIL on the right

x + 3 - 2x - 8 = x² - 3x - 4x + 12

        -x - 5 = x² - 7x + 12

             0 = x² - 6x + 17

This won't factor

Use the quadratic formula:
                  ______ 
            -b ± Öb²-4ac
        x = —————————————
                2a 

where a = 1; b = -6; c = 17

                      ______________ 
             -(-6) ± Ö(-6)²-4(1)(17)
        x = ————————————————————————
                     2(1) 
                  _____ 
             6 ± Ö36-68
        x = ————————————
                 2

                  ___ 
             6 ± Ö-32
        x = ——————————
                2

                   __ 
             6 ± iÖ32
        x = ——————————
                2 

                   ____
             6 ± iÖ16·2
        x = ————————————
                 2

                    _
             6 ± 4iÖ2
        x = ——————————
                2

                      _
             6     4iÖ2
        x = ——— ± ——————
             2      2
                   _
        x = 3 ± 2iÖ2 

Edwin