SOLUTION: x2-2x-13=0 i can not figure out how to figure this out

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Question 418439: x2-2x-13=0 i can not figure out how to figure this out
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-2x-13=0
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Use the quadratic formula:
x = [2 +- sqrt(4 -4*-13)]/2
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x = [2 +- sqrt(56)]/2
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x = [2 +- 2sqrt(14)]/2
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x = [1 +- sqrt(14)]
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Cheers,
Stan H

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-2x-13=0
Solved by pluggable solver: Quadratic Formula
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%5E2-2%2Ax-13=0 ( notice a=1, b=-2, and c=-13)





x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-13+%29%29%2F%282%2A1%29 Plug in a=1, b=-2, and c=-13




x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-13+%29%29%2F%282%2A1%29 Negate -2 to get 2




x+=+%282+%2B-+sqrt%28+4-4%2A1%2A-13+%29%29%2F%282%2A1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)




x+=+%282+%2B-+sqrt%28+4%2B52+%29%29%2F%282%2A1%29 Multiply -4%2A-13%2A1 to get 52




x+=+%282+%2B-+sqrt%28+56+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%282+%2B-+2%2Asqrt%2814%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+=+%282+%2B-+2%2Asqrt%2814%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%282+%2B+2%2Asqrt%2814%29%29%2F2 or x+=+%282+-+2%2Asqrt%2814%29%29%2F2



Now break up the fraction



x=%2B2%2F2%2B2%2Asqrt%2814%29%2F2 or x=%2B2%2F2-2%2Asqrt%2814%29%2F2



Simplify



x=1%2Bsqrt%2814%29 or x=1-sqrt%2814%29



So the solutions are:

x=1%2Bsqrt%2814%29 or x=1-sqrt%2814%29





so, x=1%2B3.74=4.14 or x=1-3.74=-2.14