The distance between the points (x,21) and (4,7) is 10sqrt(3) Find the sum of all possible values of x.

Guest Jun 1, 2022

#1**0 **

By the distance formula, we have the following equation: \(10 \sqrt 3 = \sqrt{{(x-4)}^2 + (21-7)^2}\)

Here's how to solve for x:

1 - Completely simplify the left-hand side

2 - Square both sides

3 - Subtract the left-hand side from both sides. This will now form a quadratic.

4 - Use Vieta's formula (\(-b \over a\)) to find the sum of the values of x.

BuilderBoi Jun 1, 2022