Question

Find x so the distance between (x,−1) and (4x−2,5) is 10

Answer 1

Answer:

$x = \dfrac{10}{3}~~or~~x = -2$

Step-by-step explanation:

(x,−1) and (4x−2,5) is 10

$\sqrt{(4x - 2 - x)^2 + (-1 - 5)^2} = 10$

$(3x - 2)^2 + (-6)^2 = 100$

$9x^2 - 12x + 4 + 36 = 100$

$9x^2 - 12x + 40 = 100$

$9x^2 - 12x - 60 = 0$

$3x^2 - 4x - 20 = 0$

$3x^2 - 10x + 6x - 20 = 0$

$x(3x - 10) + 2(3x - 10) = 0$

$(3x - 10)(x + 2) = 0$

$x = \dfrac{10}{3}~~or~~x = -2$