Find all 𝑥 such that the distance between the points (−5,9) and (𝑥,6) is 6.

Answer 1

distance formula, squares both sides:

(x+5)^2 + (-3)^2 = 36

(x^2 + 10x + 25) + 9 = 36 <--- FOIL

x^2 + 10x + 34 = 36

x^2 + 10x - 2 = 0

(-10 +or- sqrt ( 100 + 8))/2

(-10 +or- sqrt(108))/2 =

=(-10 +or- sqrt(2*2*3*3*3))/2

=(-10 +or- 6*sqrt(3))/2

= (-5 +or- 3*sqrt(3))

check:

(-5,9) vs (-5 + 3*sqrt(3)),6)

distance formula says;

sqrt( 27 + 9) = sqrt(36) = 6