Final answer:
To find the possible values of x in the parallelogram SHIP, where HR = 3x + 40 and RP = x^2, set HR equal to RP and solve for x. The quadratic equation x^2 - 3x - 40 = 0 can be factored to get x = 8 or x = -5.
Step-by-step explanation:
From the information given in the question, we know that HR = 3x + 40 and RP = x^2. In a parallelogram, the diagonals bisect each other. Therefore, we can set HR equal to RP and solve for x:
3x + 40 = x^2
Rearranging the equation, we get:
x^2 - 3x - 40 = 0
This is a quadratic equation, so we can factor or use the quadratic formula to solve for x. Factoring gives us:
(x - 8)(x + 5) = 0
Solving for x, we get two possible values:
x = 8 or x = -5