SOLUTION: x^2+10x+1=0 what is x?

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Question 214878: x^2+10x+1=0 what is x?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B10x%2B1=0 Start with the given equation.


Notice that the quadratic x%5E2%2B10x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=1, B=10, and C=1


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-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in A=1, B=10, and C=1


x+=+%28-10+%2B-+sqrt%28+100-4%281%29%281%29+%29%29%2F%282%281%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100-4+%29%29%2F%282%281%29%29 Multiply 4%281%29%281%29 to get 4


x+=+%28-10+%2B-+sqrt%28+96+%29%29%2F%282%281%29%29 Subtract 4 from 100 to get 96


x+=+%28-10+%2B-+sqrt%28+96+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-10+%2B-+4%2Asqrt%286%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%29%2F%282%29+%2B-+%284%2Asqrt%286%29%29%2F%282%29 Break up the fraction.


x+=+-5+%2B-+2%2Asqrt%286%29 Reduce.


x+=+-5%2B2%2Asqrt%286%29 or x+=+-5-2%2Asqrt%286%29 Break up the expression.


So the solutions are x+=+-5%2B2%2Asqrt%286%29 or x+=+-5-2%2Asqrt%286%29


which approximate to x=-0.101 or x=-9.899