Algebra

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Solve the quadratic equation.


4x^2-8x+3=5

4x² - 8x +3 - 5 = 0
4x²- 8x - 2 = 0
2x²- 4x -1 = 0

this is as far as I got. I am stuck and do not know what to do next can some one please help?





divide by two:
x²- 2x -1/2 = 0
Now add 1.5 to each side to complete the square:
x²- 2x -1/2 +1.5 = +1.5
(x-1)2=1.5
subtract 1.5 from each side
(x-1)2 -1.5 = 0

Now you have a difference of squares (1.5 is sqrt (3/2) squared..)
[x-1-sqrt3/2][x-1+sqrt3/2] = 0

divide by two:
x²- 2x -1/2 = 0
Now add 1.5 to each side to complete the square:
x²- 2x -1/2 +1.5 = +1.5
(x-1)2=1.5
subtract 1.5 from each side
(x-1)2 -1.5 = 0

Now you have a difference of squares (1.5 is sqrt (3/2) squared..)
[x-1-sqrt3/2][x-1+sqrt3/2] = 0

the answer is 0

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