Question

enter the correct value so that each expression is a perfect-square trinomial.

(x^2 - 10x + 25)

(x^2 + \text{ }x + 36)

Explanation:

Step1: Identify the perfect-square trinomial form

$$x^2 + bx + c = (x + d)^2 = x^2 + 2dx + d^2$$

Step2: Determine the value of d

$$d^2 = 36 \implies d = \pm 6$$

Step3: Calculate the coefficient b

$$b = 2d = 2(\pm 6) = \pm 12$$

Answer:

12 (or -12)