Answer:
x = 1
AB = 9
BC = 9
AC = 18
Step-by-step explanation:
Given that B is the midpoint of AC, we can say that
AB = BC
x² + 8x = 4x + 5
subtract (4x+5) from both sides to make the equation equal to 0, enabling us to solve for x
x² + 4x - 5 = 0
Because 5 and -1 add to 4 (the coefficient to x in 4x) and 5 * (-1) = -5 ( the constant), we can factor this out into
(x+5)(x-1) = 0
Therefore, x² + 8x = 4x + 5 can be true at either x=-5. x=1, or both. Plugging these values in the equations to check, starting with x=-5, we get
-5²+8(-5) =4(-5) + 5
-15 = -15
As a line segment cannot have negative length, and x² + 8x = 4x + 5 is negative when x=-5, x=-5 is not a viable solution
Next, for x=1, we get
1²+8(1) = 4(1) + 5
9=9
Therefore, x=1 is the only solution we have.
We have plugged this in for AB and BC, and 1²+8(1) = 4(1) + 5 = x² + 8x = 4x + 5 = 9 for both AB and BC
Next, AC is simply the sum of the two line segments that make them up, AB and BC, so AC = 9 + 9 = 18
