Final answer:
To find the missing value when given the modulus, square both sides of the equation to eliminate the square root, simplify, rearrange, and factor the quadratic equation to find the values of 'a'.
Step-by-step explanation:
To find the missing value when given the modulus, a-1= √37, we need to isolate the variable 'a'. Firstly, square both sides of the equation to eliminate the square root: (a-1)^2 = (√37)^2. Simplify both sides: a^2 - 2a + 1 = 37. Rearrange the equation and subtract 37 from both sides: a^2 - 2a - 36 = 0. Factor the quadratic equation: (a-6)(a+6) = 0. Therefore, a can be either 6 or -6.