SOLUTION: Please help me solve this equation: {{{ 4x^2-4x+3=0 }}}

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Question 227951: Please help me solve this equation: +4x%5E2-4x%2B3=0+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-4x%2B3=0 Start with the given equation.


Notice that the quadratic 4x%5E2-4x%2B3 is in the form of Ax%5E2%2BBx%2BC where A=4, B=-4, 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-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-4, and C=3


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


x+=+%284+%2B-+sqrt%28+16-4%284%29%283%29+%29%29%2F%282%284%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-48+%29%29%2F%282%284%29%29 Multiply 4%284%29%283%29 to get 48


x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%282%284%29%29 Subtract 48 from 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-+4i%2Asqrt%282%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%284%2B4i%2Asqrt%282%29%29%2F%288%29 or x+=+%284-4i%2Asqrt%282%29%29%2F%288%29 Break up the expression.


x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29 or x+=+%281-i%2Asqrt%282%29%29%2F%282%29 Reduce.


So the solutions are x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29 or x+=+%281-i%2Asqrt%282%29%29%2F%282%29


Note: if you have no idea what the 'i' terms are all about, then you probably haven't learned about imaginary numbers yet. If that's the case, then there are no solutions to this problem.