SOLUTION: cab you solve this quadratic equation 8x^2+1=4x

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Question 282636: cab you solve this quadratic equation 8x^2+1=4x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x%5E2%2B1=4x Start with the given equation.


8x%5E2-4x%2B1=0 Subtract 4x from both sides.


Notice that the quadratic 8x%5E2-4x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=8, 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%288%29%281%29+%29%29%2F%282%288%29%29 Plug in A=8, B=-4, and C=1


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%288%29%281%29+%29%29%2F%282%288%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%288%29%281%29+%29%29%2F%282%288%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-32+%29%29%2F%282%288%29%29 Multiply 4%288%29%281%29 to get 32


x+=+%284+%2B-+sqrt%28+-16+%29%29%2F%282%288%29%29 Subtract 32 from 16 to get -16


x+=+%284+%2B-+sqrt%28+-16+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


x+=+%284+%2B-+4%2Ai%29%2F%2816%29 Take the square root of -16 to get 4%2Ai.


x+=+%284+%2B+4%2Ai%29%2F%2816%29 or x+=+%284+-+4%2Ai%29%2F%2816%29 Break up the expression.


x+=+%284%29%2F%2816%29+%2B+%284%2Ai%29%2F%2816%29 or x+=++%284%29%2F%2816%29+-+%284%2Ai%29%2F%2816%29 Break up the fraction for each case.


x+=+1%2F4%2B%281%2F4%29%2Ai or x+=+1%2F4-%281%2F4%29%2Ai Reduce.


So the solutions are x+=+1%2F4%2B%281%2F4%29%2Ai or x+=+1%2F4-%281%2F4%29%2Ai