Answer:
[tex] x = \dfrac{10}{3}~~or~~x = -2 [/tex]
Step-by-step explanation:
(x,−1) and (4x−2,5) is 10
[tex] \sqrt{(4x - 2 - x)^2 + (-1 - 5)^2} = 10 [/tex]
[tex] (3x - 2)^2 + (-6)^2 = 100 [/tex]
[tex] 9x^2 - 12x + 4 + 36 = 100 [/tex]
[tex] 9x^2 - 12x + 40 = 100 [/tex]
[tex] 9x^2 - 12x - 60 = 0 [/tex]
[tex] 3x^2 - 4x - 20 = 0 [/tex]
[tex] 3x^2 - 10x + 6x - 20 = 0 [/tex]
[tex] x(3x - 10) + 2(3x - 10) = 0 [/tex]
[tex] (3x - 10)(x + 2) = 0 [/tex]
[tex] x = \dfrac{10}{3}~~or~~x = -2 [/tex]
