SOLUTION: please help me solve this equation: {{{4x^2=x}}}

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Question 223419: please help me solve this equation: 4x%5E2=x
Found 3 solutions by jim_thompson5910, ankor@dixie-net.com, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


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


Notice that the quadratic 4x%5E2-x is in the form of Ax%5E2%2BBx%2BC where A=4, B=-1, and C=0


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%284%29%280%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-1, and C=0


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%284%29%280%29+%29%29%2F%282%284%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%284%29%280%29+%29%29%2F%282%284%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-0+%29%29%2F%282%284%29%29 Multiply 4%284%29%280%29 to get 0


x+=+%281+%2B-+sqrt%28+1+%29%29%2F%282%284%29%29 Subtract 0 from 1 to get 1


x+=+%281+%2B-+sqrt%28+1+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%281+%2B-+1%29%2F%288%29 Take the square root of 1 to get 1.


x+=+%281+%2B+1%29%2F%288%29 or x+=+%281+-+1%29%2F%288%29 Break up the expression.


x+=+%282%29%2F%288%29 or x+=++%280%29%2F%288%29 Combine like terms.


x+=+1%2F4 or x+=+0 Simplify.


So the solutions are x+=+1%2F4 or x+=+0


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2+=+x
Subtract x from both sides
4x%5E2+-+x+=+0
Factor out x
x%284x+-+1%29+=+0
Two solutions
x = 0
and
4x = +1
x = 1%2F4
:
Check this solution in original equation
4%281%2F4%29%5E2+=+%281%2F4%29
:
4%281%2F16%29+=+%281%2F4%29
:
%284%2F16%29+=+%281%2F4%29

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
4x%5E2+=+x Divide both sides by x.
4x%5E2%2Fx+=+x%2Fx Simplify.
4x+=+1 Divide both sides by 4.
cross%284%29x%2Fcross%284%29+=+1%2F4 Simplify.
highlight%28x+=+1%2F4%29