Posted by **Jess** on Tuesday, July 10, 2007 at 3:35am.

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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