SOLUTION: How do i work out 16x2-8x+1=0 and also 2x2=4x+1

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Question 334995: How do i work out 16x2-8x+1=0 and also 2x2=4x+1
Found 2 solutions by jim_thompson5910, checkley77:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Get every term to one side and use the quadratic formula to solve for 'x'. I'll work out the first problem. I'm using this solver


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 16%2Ax%5E2-8%2Ax%2B1=0 ( notice a=16, b=-8, and c=1)





x+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A16%2A1+%29%29%2F%282%2A16%29 Plug in a=16, b=-8, and c=1




x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A16%2A1+%29%29%2F%282%2A16%29 Negate -8 to get 8




x+=+%288+%2B-+sqrt%28+64-4%2A16%2A1+%29%29%2F%282%2A16%29 Square -8 to get 64 (note: remember when you square -8, you must square the negative as well. This is because %28-8%29%5E2=-8%2A-8=64.)




x+=+%288+%2B-+sqrt%28+64%2B-64+%29%29%2F%282%2A16%29 Multiply -4%2A1%2A16 to get -64




x+=+%288+%2B-+sqrt%28+0+%29%29%2F%282%2A16%29 Combine like terms in the radicand (everything under the square root)




x+=+%288+%2B-+0%29%2F%282%2A16%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%288+%2B-+0%29%2F32 Multiply 2 and 16 to get 32


So now the expression breaks down into two parts


x+=+%288+%2B+0%29%2F32 or x+=+%288+-+0%29%2F32


Lets look at the first part:


x=%288+%2B+0%29%2F32


x=8%2F32 Add the terms in the numerator

x=1%2F4 Divide


So one answer is

x=1%2F4




Now lets look at the second part:


x=%288+-+0%29%2F32


x=8%2F32 Subtract the terms in the numerator

x=1%2F4 Divide


So another answer is

x=1%2F4


So our solutions are:

x=1%2F4 or x=1%2F4


which means we only have one solution


x=1%2F4






Again, if you need more help with the quadratic formula, see this solver

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
16x^2-8x+1=0
(4x-1)(4x-1)=0
4x-1=0
4x=1
x-1/4 ans.
----------------
2x^2=4x+1
2x^2-4x-1)=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(4+-sqrt[-4^2-4*2*-1])/2*2
x=(4+-sqrt[16+8])/4
x=(4+-sqrt24)/4
x=(4+-4.9)/4
x=4+4.9)/4
x=8.9/4
x=2.25 ans.
x=(4-4.9)/4
x=-.9/4
x=.225 ans.