SOLUTION: {{{x^3-x^2}}}{{{""=""}}}{{{18}}}

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Question 1032754: x%5E3-x%5E2%22%22=%22%2218
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3-x%5E2%22%22=%22%2218

x%5E3-x%5E2-18%22%22=%22%220

x%5E3-x%5E2%2B0x-18%22%22=%22%220

Potential rational solutions: ±1,±3,±6,±9,±18

3|1 -1  0 -18
 |   3  6  18
  1  2  6   0

We have factored the polynomial as

%28x-3%29%28x%5E2%2B2x%2B6%29%22%22=%22%220

Use zero-factor property:

x-3%22%22=%22%220; x%5E2%2B2x%2B6%22%22=%22%220

x%22%22=%22%223;   x%22%22=%22%22%28-b+%2B-+sqrt%28b%5E2-4ac+%29%29%2F%282a%29+

                  x%22%22=%22%22%28-2+%2B-+sqrt%282%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29+
                  x%22%22=%22%22%28-2+%2B-+sqrt%284-24%29%29%2F2+
                  x%22%22=%22%22%28-2+%2B-+sqrt%28-20%29%29%2F2+
                  x%22%22=%22%22%28-2+%2B-+i%2Asqrt%2820%29%29%2F2+
                  x%22%22=%22%22%28-2+%2B-+i%2Asqrt%284%2A5%29%29%2F2+
                  x%22%22=%22%22%28-2+%2B-+2i%2Asqrt%285%29%29%2F2+
                  x%22%22=%22%22-2%2F2+%2B-+2i%2Asqrt%285%29%2F2+
                  x%22%22=%22%22-1+%2B-+i%2Asqrt%285%29+

Solution set  

Edwin