SOLUTION: Use the quadratic formula to solve the equation. x^2-x= -10

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the quadratic formula to solve the equation. x^2-x= -10      Log On


   

Question 557710: Use the quadratic formula to solve the equation.
x^2-x= -10
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x=-10 Start with the given equation.


x%5E2-x%2B10=0 Get every term to the left side.


Notice that the quadratic x%5E2-x%2B10 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=10


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%2810%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=10


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%2810%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-40+%29%29%2F%282%281%29%29 Multiply 4%281%29%2810%29 to get 40


x+=+%281+%2B-+sqrt%28+-39+%29%29%2F%282%281%29%29 Subtract 40 from 1 to get -39


x+=+%281+%2B-+sqrt%28+-39+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+i%2Asqrt%2839%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%2839%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2839%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%281%2Bi%2Asqrt%2839%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2839%29%29%2F%282%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+-+x+=+-10+
+x%5E2+-+x+%2B+10+=+0+
This is in the form
+ax%5E2+%2B+bx+%2B+c+=+0+
so I can use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-1+
+c+=+10+
x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29+
x+=+%28+1+%2B-+sqrt%28+1+-+40+%29%29+%2F+2+
x+=+%28+1+%2B-+sqrt%28+-39+%29%29+%2F+2+
x+=+%28+1+%2B-+sqrt%28+-1+%29%2Asqrt%2839%29+%29+%2F+2+
+x+=+%28+1+%2B+sqrt%2839%29%2Ai+%29+%2F+2+
and
+x+=+%28+1+-+sqrt%2839%29%2Ai+%29+%2F+2+
------------------------
Check answer:
+x%5E2+=+%28%28+1+-+sqrt%2839%29%2Ai+%29+%2F+2%29%5E2+
+x%5E2+=+%28+1+-+2%2Asqrt%2839%29%2Ai+-+39+%29+%2F+4+

+x%5E2+-+x+=+%281%2F4%29%2A%28+-38+-+2+%29+
+x%5E2+-+x+=+-10+
OK