Answer:
The values of x are
[tex]x=-1.5\ , 0.5[/tex]
Step-by-step explanation:
we have
[tex]4x^{2}+4x-3=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]4x^{2}+4x=3[/tex]
Factor the leading coefficient
[tex]4(x^{2}+x)=3[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]4(x^{2}+x+.25)=3+1[/tex]
[tex]4(x^{2}+x+.25)=4[/tex]
[tex](x^{2}+x+.25)=1[/tex]
Rewrite as perfect squares
[tex](x+0.5)^{2}=1[/tex]
Square root both sides
[tex]x+0.5=(+/-)1[/tex]
[tex]x=-0.5(+/-)1[/tex]
[tex]x=-0.5+1=0.5[/tex]
[tex]x=-0.5-1=-1.5[/tex]
