SOLUTION: t^2 +10t + 26 = 0

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Question 299452: t^2 +10t + 26 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
t%5E2%2B10t%2B26=0 Start with the given equation.


Notice that the quadratic t%5E2%2B10t%2B26 is in the form of At%5E2%2BBt%2BC where A=1, B=10, and C=26


Let's use the quadratic formula to solve for "t":


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


t+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%281%29%2826%29+%29%29%2F%282%281%29%29 Plug in A=1, B=10, and C=26


t+=+%28-10+%2B-+sqrt%28+100-4%281%29%2826%29+%29%29%2F%282%281%29%29 Square 10 to get 100.


t+=+%28-10+%2B-+sqrt%28+100-104+%29%29%2F%282%281%29%29 Multiply 4%281%29%2826%29 to get 104


t+=+%28-10+%2B-+sqrt%28+-4+%29%29%2F%282%281%29%29 Subtract 104 from 100 to get -4


t+=+%28-10+%2B-+sqrt%28+-4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


t+=+%28-10+%2B-+2%2Ai%29%2F%282%29 Take the square root of -4 to get 2%2Ai.


t+=+%28-10+%2B+2%2Ai%29%2F%282%29 or t+=+%28-10+-+2%2Ai%29%2F%282%29 Break up the expression.


t+=+%28-10%29%2F%282%29+%2B+%282%2Ai%29%2F%282%29 or t+=++%28-10%29%2F%282%29+-+%282%2Ai%29%2F%282%29 Break up the fraction for each case.


t+=+-5%2B1%2Ai or t+=+-5-i Reduce.


So the solutions are t+=+-5%2Bi or t+=+-5-i