solve by completing the square 4X^2 + 2X – 3 = 0 Im stuck on this problem someone please help?

Question

solve by completing the square 4X^2 + 2X – 3 = 0

Answer 1

4x^2 + 2x - 3 = 0
4x^2 + 2x = 3
x^2 + (1/2)x = 3/4
x^2 + (1/2)x + (1/4)^2 = 3/4 + (1/4)^2
(x + 1/4)^2 = 13/16
x + 1/4 = +/- sqrt(13/16)
x + 1/4 = +/- sqrt(13) / 4
x = -1/4 +/- sqrt(13) / 4
x = (-1 +/- sqrt(13)) / 4

Answer 2

Divide all terms by 4 because you need a coefficient of 1 in front of the x^2.
x^2+(1/2)x-(3/4)=0 Move 3/4 to the right side.
x^2+(1/2)x=(3/4)
Take (b/2)^2 so ((1/2)/2)^2
(1/2)/2= (1/2)x(1/2) Due to division of fractions. so it equals 1/4. Then square it 1/16.
Add 1/16 to both sides.
x^2+(1/2)x+(1/16)=(3/4)+(1/16) Factor the left side into a binomial.
(x+1/4)^2=12/16+1/16
(x+1/4)^2=13/16
Square root both sides.
sqrt[(x+1/4)^2]=sqrt[13/16]
x+1/4=+/- sqrt(13)/sqrt(16)
x+1/4=+/- sqrt(13)/4
x=-1/4 +/- sqrt (13)/4
or
x=[-1+/- sqrt(13)]/4

Answer 3

4X^2 + 2X – 3 = 0

add 3 for both sides
4x^2 + 2x = 3

divide 4 for both sides
x^2 + 1/2x = 3/4

apply (b/2)^2
x^2 + 1/2x + ( 1/2 / 2)^2 = 3/4 + ( 1/2 / 2)^2

x^2 + 1/2x + 1/16 = 3/4 + 1/16

x^2 + 1/2x + 1/16 = 13/16

factor
(x+1/4)^2 = 13/16

take a square root
x+1/4 = +/- sqrt(13)/4

subtract 1/4
x = -1/4 +/- sqrt(13)/4

Answer 4

x² + (1/2).x - 3/4 = 0
(x² + (1/2).x +1/16) - 1/16 - 3/4 = 0
(x +1/4)² = 13/16
x + 1/4 = ± √13 / 4
x = (√13 - 1) / 4, x = - (√13 + 1) / 4

Answer 5

x1=(-1+sqr(13))/4
x2=(-1-sqr(13))/4