SOLUTION: x^2-14x-6=0

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Question 684660: x^2-14x-6=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-14x-6=0 Start with the given equation.


Notice that the quadratic x%5E2-14x-6 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-14, and C=-6


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-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-14, and C=-6


x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Negate -14 to get 14.


x+=+%2814+%2B-+sqrt%28+196-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Square -14 to get 196.


x+=+%2814+%2B-+sqrt%28+196--24+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-6%29 to get -24


x+=+%2814+%2B-+sqrt%28+196%2B24+%29%29%2F%282%281%29%29 Rewrite sqrt%28196--24%29 as sqrt%28196%2B24%29


x+=+%2814+%2B-+sqrt%28+220+%29%29%2F%282%281%29%29 Add 196 to 24 to get 220


x+=+%2814+%2B-+sqrt%28+220+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2814+%2B-+2%2Asqrt%2855%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2814%29%2F%282%29+%2B-+%282%2Asqrt%2855%29%29%2F%282%29 Break up the fraction.


x+=+7+%2B-+sqrt%2855%29 Reduce.


x+=+7%2Bsqrt%2855%29 or x+=+7-sqrt%2855%29 Break up the expression.


So the two exact solutions are x+=+7%2Bsqrt%2855%29 or x+=+7-sqrt%2855%29