SOLUTION: x^2-6x+10=0

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Question 202597: x^2-6x+10=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x%2B10=0 Start with the given equation.


Notice that the quadratic x%5E2-6x%2B10 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-6, and C=10


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%2810%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-6, and C=10


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%2810%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-40+%29%29%2F%282%281%29%29 Multiply 4%281%29%2810%29 to get 40


x+=+%286+%2B-+sqrt%28+-4+%29%29%2F%282%281%29%29 Subtract 40 from 36 to get -4


x+=+%286+%2B-+sqrt%28+-4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


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


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


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


x+=+3%2Bi or x+=++3-i Reduce.


So the solutions are x+=+3%2Bi or x+=++3-i