Final answer:
The positive value of x is found by setting the lengths of ZW and WY equal to each other, resulting in a quadratic equation. After solving the equation, the positive value of x is determined to be 10.
Step-by-step explanation:
The student is asked to find the positive value of x given that line segment ZY contains the midpoint W, with ZW having a length expressed by the quadratic equation x2 – 5x – 20 and WY having a length expressed by the linear equation 3x. Since W is the midpoint, ZW and WY must be equal. Therefore, we can set up the equation x2 – 5x – 20 = 3x and solve for x.
Step 1: Set the quadratic equation equal to the linear equation to find x.
x2 – 5x – 20 = 3x
Step 2: Subtract 3x from both sides of the equation to set the equation to zero.
x2 – 8x – 20 = 0
Step 3: Factor the quadratic equation (or use the quadratic formula).
(x - 10)(x + 2) = 0
Step 4: Set each factor equal to zero and solve for x.
x - 10 = 0 or x + 2 = 0
Step 5: Solve each equation for x.
x = 10 or x = -2
Since we are looking for the positive value of x, the solution is x = 10.