SOLUTION: Use the quadratic formula to solve the following quadratic equation x^2- 4x+ 2 =0

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Question 112160: Use the quadratic formula to solve the following quadratic equation
x^2- 4x+ 2 =0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-4%2Ax%2B2=0 ( notice a=1, b=-4, and c=2)





x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=2




x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Negate -4 to get 4




x+=+%284+%2B-+sqrt%28+16-4%2A1%2A2+%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%2B-8+%29%29%2F%282%2A1%29 Multiply -4%2A2%2A1 to get -8




x+=+%284+%2B-+sqrt%28+8+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%284+%2B-+2%2Asqrt%282%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%282%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%284+%2B+2%2Asqrt%282%29%29%2F2 or x+=+%284+-+2%2Asqrt%282%29%29%2F2



Now break up the fraction



x=%2B4%2F2%2B2%2Asqrt%282%29%2F2 or x=%2B4%2F2-2%2Asqrt%282%29%2F2



Simplify



x=2%2Bsqrt%282%29 or x=2-sqrt%282%29



So the solutions are:

x=2%2Bsqrt%282%29 or x=2-sqrt%282%29