SOLUTION: Hi! I was trying to solve this problem for quadratic equation: {{{ x^2-2x+5=0}}} but in order to simplify it I get stuck on the part during the equation that looks like this (the +

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi! I was trying to solve this problem for quadratic equation: {{{ x^2-2x+5=0}}} but in order to simplify it I get stuck on the part during the equation that looks like this (the +      Log On


   

Question 451301: Hi! I was trying to solve this problem for quadratic equation: +x%5E2-2x%2B5=0 but in order to simplify it I get stuck on the part during the equation that looks like this (the + sign in the equation represents the + or - one in the actual equation: +2%2B+sqrt%28+-+24+%29%2F2. I know that the square root of a negative number is (square root of the number as if it were positive) x i(the square root of - 1). I also know that there will be 2 solutions to this equation. But what do I do after +2%2B+sqrt%28+-+24+%29%2F2 if I need to simplify it as much as possible? Thanks for any help you may give me!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-2x%2B5=0 Start with the given equation.


Notice that the quadratic x%5E2-2x%2B5 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-2, and C=5


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=5


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%285%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4-20+%29%29%2F%282%281%29%29 Multiply 4%281%29%285%29 to get 20


x+=+%282+%2B-+sqrt%28+-16+%29%29%2F%282%281%29%29 Subtract 20 from 4 to get -16 (this is where you made your mistake).


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


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


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


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


x+=+1%2B2%2Ai or x+=++1-2%2Ai Reduce.


So the solutions are x+=+1%2B2%2Ai or x+=+1-2%2Ai

For more help with the quadratic formula, see this solver.