SOLUTION: Solve {{{x^2-x+10=0}}}

Algebra ->  Graphs -> SOLUTION: Solve {{{x^2-x+10=0}}}      Log On


   

Question 130697: Solve

x%5E2-x%2B10=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2-x%2B10=0 ( notice a=1, b=-1, and c=10)




x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Plug in a=1, b=-1, and c=10



x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Negate -1 to get 1



x+=+%281+%2B-+sqrt%28+1-4%2A1%2A10+%29%29%2F%282%2A1%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)



x+=+%281+%2B-+sqrt%28+1%2B-40+%29%29%2F%282%2A1%29 Multiply -4%2A10%2A1 to get -40



x+=+%281+%2B-+sqrt%28+-39+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%281+%2B-+i%2Asqrt%2839%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%281+%2B-+i%2Asqrt%2839%29%29%2F%282%29 Multiply 2 and 1 to get 2



After simplifying, the quadratic has roots of

x=1%2F2+%2B+%28sqrt%2839%29%2F2%29%2Ai or x=1%2F2+-+%28sqrt%2839%29%2F2%29%2Ai