SOLUTION: Solve: x^2 - x + 49 = 0 since b^2-4ac is negative, this has imaginary roots. I would like to know if there is a better/easier way to solve this and such quadratics..many thanks

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve: x^2 - x + 49 = 0 since b^2-4ac is negative, this has imaginary roots. I would like to know if there is a better/easier way to solve this and such quadratics..many thanks      Log On


   

Question 236647: Solve: x^2 - x + 49 = 0
since b^2-4ac is negative, this has imaginary roots. I would like to know if there is a better/easier way to solve this and such quadratics..many thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x%2B49=0 Start with the given equation.


Notice that the quadratic x%5E2-x%2B49 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=49


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%2849%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=49


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%2849%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%2849%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-196+%29%29%2F%282%281%29%29 Multiply 4%281%29%2849%29 to get 196


x+=+%281+%2B-+sqrt%28+-195+%29%29%2F%282%281%29%29 Subtract 196 from 1 to get -195


x+=+%281+%2B-+sqrt%28+-195+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+i%2Asqrt%28195%29%29%2F%282%29 Simplify the square root


x+=+%281%2Bi%2Asqrt%28195%29%29%2F%282%29 or x+=+%281-i%2Asqrt%28195%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%281%2Bi%2Asqrt%28195%29%29%2F%282%29 or x+=+%281-i%2Asqrt%28195%29%29%2F%282%29