SOLUTION: 4x^2-4x=1

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Question 193113: 4x^2-4x=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-4x=1 Start with the given equation.


4x%5E2-4x-1=0 Subtract 1 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=-4, 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-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-4, and c=-1


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16--16+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-1%29 to get -16


x+=+%284+%2B-+sqrt%28+16%2B16+%29%29%2F%282%284%29%29 Rewrite sqrt%2816--16%29 as sqrt%2816%2B16%29


x+=+%284+%2B-+sqrt%28+32+%29%29%2F%282%284%29%29 Add 16 to 16 to get 32


x+=+%284+%2B-+sqrt%28+32+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%284+%2B-+4%2Asqrt%282%29%29%2F%288%29 Simplify the square root


x+=+%284%2B4%2Asqrt%282%29%29%2F%288%29 or x+=+%284-4%2Asqrt%282%29%29%2F%288%29 Break up the expression.


x+=+%281%2Bsqrt%282%29%29%2F%282%29 or x+=+%281-sqrt%282%29%29%2F%282%29 Reduce


So the answers are x+=+%281%2Bsqrt%282%29%29%2F%282%29 or x+=+%281-sqrt%282%29%29%2F%282%29


which approximate to x=1.207 or x=-0.207