Answer:
The value of [tex]x[/tex] is [tex]\frac{25}{2}[/tex].
Step-by-step explanation:
From Analytical Geometry we get that ratio of BC to BE is:
[tex]\frac{BC}{BE} = 2[/tex] (From definition of midpoint)
[tex]\frac{BE+CE}{BE} = 2[/tex]
[tex]1 + \frac{CE}{BE} = 2[/tex]
[tex]\frac{CE}{BE} = 1[/tex]
[tex]CE = BE[/tex]
If we know that [tex]BE = 50[/tex] and [tex]CE = 2\cdot x + 25[/tex], then, the equality above is expanded:
[tex]2\cdot x +25 = 50[/tex]
[tex]2\cdot x = 25[/tex]
[tex]x = \frac{25}{2}[/tex]
The value of [tex]x[/tex] is [tex]\frac{25}{2}[/tex].
