Explanation:
The coordinates are given below as
[tex]\begin{gathered} (x,-7),(-4,-2) \\ d=\sqrt{89} \end{gathered}[/tex]
Concept:
The distance formula to be used is given below as
[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
By substituing the values, we will have
[tex]\begin{gathered} d^{2}=(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} \\ (\sqrt{89})^2=(-4-x)^2+(-2-(-7)^2 \\ 89=(-4-x)^2+(-2+7)^2 \\ 89=(-4-x)^2+(5^2) \\ 89=(-4-x)^2+25 \\ (-4-x)^2=89-25 \\ (-4-x)^2=64 \end{gathered}[/tex]
Square root both sides, we will have
[tex]\begin{gathered} (-4-x)^2=64 \\ -4-x=\sqrt{64} \\ -4-x=\pm8 \\ x=-4\pm8 \\ x=-4+8,x=-4-8 \\ x=4,x=-12 \end{gathered}[/tex]
Hence,
The final answers are
[tex]x=-12,4[/tex]
