SOLUTION: solutions to the problem 4x^2-8x+3=0

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Question 342746: solutions to the problem 4x^2-8x+3=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-8x%2B3=0 Start with the given equation.


Notice that the quadratic 4x%5E2-8x%2B3 is in the form of Ax%5E2%2BBx%2BC where A=4, B=-8, and C=3


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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-8, and C=3


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%284%29%283%29+%29%29%2F%282%284%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-48+%29%29%2F%282%284%29%29 Multiply 4%284%29%283%29 to get 48


x+=+%288+%2B-+sqrt%28+16+%29%29%2F%282%284%29%29 Subtract 48 from 64 to get 16


x+=+%288+%2B-+sqrt%28+16+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%288+%2B-+4%29%2F%288%29 Take the square root of 16 to get 4.


x+=+%288+%2B+4%29%2F%288%29 or x+=+%288+-+4%29%2F%288%29 Break up the expression.


x+=+%2812%29%2F%288%29 or x+=++%284%29%2F%288%29 Combine like terms.


x+=+3%2F2 or x+=+1%2F2 Simplify.


So the solutions are x+=+3%2F2 or x+=+1%2F2


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Jim