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