SOLUTION: x^2+x-110=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: x^2+x-110=0      Log On


   

Question 549807: x^2+x-110=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2Bx-110=0 Start with the given equation.


Notice that the quadratic x%5E2%2Bx-110 is in the form of Ax%5E2%2BBx%2BC where A=1, B=1, and C=-110


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-110%29+%29%29%2F%282%281%29%29 Plug in A=1, B=1, and C=-110


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-110%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--440+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-110%29 to get -440


x+=+%28-1+%2B-+sqrt%28+1%2B440+%29%29%2F%282%281%29%29 Rewrite sqrt%281--440%29 as sqrt%281%2B440%29


x+=+%28-1+%2B-+sqrt%28+441+%29%29%2F%282%281%29%29 Add 1 to 440 to get 441


x+=+%28-1+%2B-+sqrt%28+441+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+21%29%2F%282%29 Take the square root of 441 to get 21.


x+=+%28-1+%2B+21%29%2F%282%29 or x+=+%28-1+-+21%29%2F%282%29 Break up the expression.


x+=+%2820%29%2F%282%29 or x+=++%28-22%29%2F%282%29 Combine like terms.


x+=+10 or x+=+-11 Simplify.


So the solutions are x+=+10 or x+=+-11