The formula to find the distance between two points is:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where }(x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points.} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} (x_1,y_1)=(x,3) \\ (x_2,y_2)=(-7,6) \\ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \sqrt{10}=\sqrt{(-7-x)^2+(6-3)^2} \\ $\text{ Square both sides of the equation}$ \\ (\sqrt{10})^2=(\sqrt{(-7-x)^2+(6-3)^2})^2 \\ 10=(-7-x)^2+(6-3)^2 \\ 10=(-7-x)^2+3^2 \\ 10=(-7-x)^2+9 \\ \text{ Subtract 9 from both sides} \\ 10-9=(-7-x)^2+9-9 \\ 1=(-7-x)^2 \\ $\text{ Apply square root to both sides of the equation}$ \\ \sqrt{1}=\sqrt{(-7-x)^2} \\ 1=-7-x \\ \text{ Add 7 from both sides} \\ 1+7=-7-x+7 \\ 8=-x \\ \text{ Multiply by -1 from both sides} \\ 8*-1=-x*-1 \\ -8=x \end{gathered}[/tex]Therefore, the value of x that satisfies the given conditions is -8.
Answer[tex]x=-8[/tex]