We have the equation:
[tex]8x=-4-4x^2[/tex]We want to find the values of x that satisfy the equation.
We can see the equation corresponds to a parabola, and this is the equation of the roots, so re write the equation in the standard form and find the roots:
[tex]\begin{gathered} 0=-4x^2+8x-4 \\ \text{Dividing all by -4:} \\ 0=x^2-2x+1=(x-1)^2 \end{gathered}[/tex]So the equation above has a solution when x=1, and it's the unique solution.
