Answer :
First, let's use the distance formula to calculate the distance between P and (-1, 0):
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\ \\ d=\sqrt{(0-y)^2+(-1-x)^2}\\ \\ \frac{4}{5}=\sqrt{y^2+x^2+2x+1} \\ (\frac{4}{5})^2=x^2+y^2+2x+1 \end{gathered}[/tex]Since point P is on the given circle, let's subtract the equation above from the circle equation, then we solve the resulting equation for x:
[tex]\begin{gathered} x^2+y^2+2x+1-(x^2+y^2)=(\frac{4}{5})^2-(1)\\ \\ 2x+1=\frac{16}{25}-1\\ \\ 2x=\frac{16}{25}-2\\ \\ x=\frac{8}{25}-1=\frac{8}{25}-\frac{25}{25}=-\frac{17}{25} \end{gathered}[/tex]Therefore the x-coordinate of P is -17/25.