The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)#

Substituting the information from the problem and solving for #a# gives:

#sqrt(50) = sqrt((color(red)(a) - color(blue)(-4))^2 + (color(red)(8) - color(blue)(1))^2)#

#sqrt(50) = sqrt((color(red)(a) + color(blue)(4))^2 + (color(red)(8) - color(blue)(1))^2)#

#sqrt(50) = sqrt((color(red)(a) + color(blue)(4))^2 + 7^2)#

#sqrt(50) = sqrt(a^2 + 8a + 16 + 49)#

#sqrt(50) = sqrt(a^2 + 8a + 65)#

#(sqrt(50))^2 = (sqrt(a^2 + 8a + 65))^2#

#50 = a^2 + 8a + 65#

#50 - color(red)(50) = a^2 + 8a + 65 - color(red)(50)#

#0 = a^2 + 8a + 15#

#0 = (a + 3)(a + 5)#

**Solution 1:**

#a + 3 = 0#

#a + 3 - color(red)(3) = 0 - color(red)(3)#

#a + 0 = -3#

#a = -3#

**Solution 2:**

#a + 5 = 0#

#a + 5 - color(red)(5) = 0 - color(red)(5)#

#a + 0 = -5#

#a = -5#

**The Solution Is:**

#color(red)(a)# can be either #-3# or #-5# for the two points to have a distance of #sqrt(50)#