In the diagram below B is the midpoint of AC if AB equals 2X and BC equals X squared -24 find the value of X and the length of AC

B is the midpoint, so AB = BC; solve for x, which is 4. Then substitute 4 into 3x+2 (which is DE) and get 14.

Step-by-step explanation:

  x = 6

  AC = 24

Step-by-step explanation:

The midpoint divides the segment into two congruent parts.

  AB = BC

  BC -AB = 0

  x^2 -24 -2x = 0

  (x -1)^2 = 25 . . . . . . add 25, write as a square

  x = 1 +√25 = 6 . . . . only the positive solution is of interest.

AC = 2(AB) = 2(2x) = 4(6) = 24

The value of X is 6, and the length of AC is 24 units.