SOLUTION: helpp!! use the quadratic formula x=-b+(small line under the plus sign) sqrt(b^2-4ac)/2a to find the root of the equation x^2-4x-6=0 thank you for your help

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Question 140865: helpp!! use the quadratic formula x=-b+(small line under the plus sign) sqrt(b^2-4ac)/2a to find the root of the equation
x^2-4x-6=0 thank you for your help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-4%2Ax-6=0 ( notice a=1, b=-4, and c=-6)




x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=-6



x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Negate -4 to get 4



x+=+%284+%2B-+sqrt%28+16-4%2A1%2A-6+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)



x+=+%284+%2B-+sqrt%28+16%2B24+%29%29%2F%282%2A1%29 Multiply -4%2A-6%2A1 to get 24



x+=+%284+%2B-+sqrt%28+40+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%284+%2B-+2%2Asqrt%2810%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+=+%284+%2B-+2%2Asqrt%2810%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%284+%2B+2%2Asqrt%2810%29%29%2F2 or x+=+%284+-+2%2Asqrt%2810%29%29%2F2


Now break up the fraction


x=%2B4%2F2%2B2%2Asqrt%2810%29%2F2 or x=%2B4%2F2-2%2Asqrt%2810%29%2F2


Simplify


x=2%2Bsqrt%2810%29 or x=2-sqrt%2810%29


So these expressions approximate to

x=5.16227766016838 or x=-1.16227766016838


So our solutions are:
x=5.16227766016838 or x=-1.16227766016838

Notice when we graph x%5E2-4%2Ax-6, we get:



when we use the root finder feature on a calculator, we find that x=5.16227766016838 and x=-1.16227766016838.So this verifies our answer