Final answer:
To find the intermediate step while completing the square for the equation x² + 37 = -14x - 8, rearrange the terms and add (14/2)² to both sides. This results in the intermediate form (x + 7)² = 4, where the left-hand side is now a perfect square trinomial.
Step-by-step explanation:
To find the intermediate step in the form (x + a)² = b while completing the square for the equation x² + 37 = -14x - 8, we first rearrange the terms to set the equation up for completing the square:
x² + 14x = -37 - 8
x² + 14x = -45
Next, we need to find the value that makes the left-hand side a perfect square trinomial. This value is (b/2)², where 'b' is the coefficient of 'x'. Here, 'b' is 14, so we calculate (14/2)² which equals 49. We add this value to both sides of the equation:
x² + 14x + 49 = 49 - 45
x² + 14x + 49 = 4
The left-hand side is now a perfect square trinomial and can be written as the square of a binomial:
(x + 7)² = 4
This step is the intermediate step in the form (x + a)² = b.