The distance between two points is √39 . one endpoint is (4,−3) . it is known that the y-coordinate of the other endpoint is 2.

what is the x-coordinate of this endpoint? (more than one answer)
choices:
a). 2√7
b). 2
c). 4-√14
d). 4+√14
e). 10
f). -6

Using the formula for the distance between two points, it is found that the x-coordinate of the endpoint can be of:

, options C and D.

The distance between two points, and , is given by:

In this problem, points (4, -3) and (x, 2), with a distance of units. Thus:

Quadratic equation with coefficients , thus:

Options C and D.

A similar problem is given at link

C & D

Step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .