SOLUTION: Can you please help me understand how to do this problem. Solve for X x^2 - x + 11 = 0 so x = ? I came up with this answer and I am unsure if it is correct. 1 + sqrt

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can you please help me understand how to do this problem. Solve for X x^2 - x + 11 = 0 so x = ? I came up with this answer and I am unsure if it is correct. 1 + sqrt      Log On


   

Question 352771: Can you please help me understand how to do this problem.
Solve for X
x^2 - x + 11 = 0 so x = ?
I came up with this answer and I am unsure if it is correct.
1 + sqrt43 over 2
1 - sqrt42 over 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x%2B11=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-1, and c=11


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%2811%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=11


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%2811%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%2811%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-44+%29%29%2F%282%281%29%29 Multiply 4%281%29%2811%29 to get 44


x+=+%281+%2B-+sqrt%28+-43+%29%29%2F%282%281%29%29 Subtract 44 from 1 to get -43


x+=+%281+%2B-+sqrt%28+-43+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+i%2Asqrt%2843%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%281%2Bi%2Asqrt%2843%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2843%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%281%2Bi%2Asqrt%2843%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2843%29%29%2F%282%29