SOLUTION: x^2-6x+13=0

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Question 339009: x^2-6x+13=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x%2B13=0 Start with the given equation.


Notice that the quadratic x%5E2-6x%2B13 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-6, and C=13


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%2813%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-6, and C=13


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%2813%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%2813%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-52+%29%29%2F%282%281%29%29 Multiply 4%281%29%2813%29 to get 52


x+=+%286+%2B-+sqrt%28+-16+%29%29%2F%282%281%29%29 Subtract 52 from 36 to get -16


x+=+%286+%2B-+sqrt%28+-16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+4%2Ai%29%2F%282%29 Take the square root of -16 to get 4%2Ai.


x+=+%286+%2B+4%2Ai%29%2F%282%29 or x+=+%286+-+4%2Ai%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29+%2B+%284%2Ai%29%2F%282%29 or x+=++%286%29%2F%282%29+-+%284%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+3%2B2%2Ai or x+=++3-2%2Ai Reduce.


x+=+3%2B2%2Ai or x+=+3-2%2Ai Simplify.


So the solutions are x+=+3%2B2%2Ai or x+=+3-2%2Ai


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim