Final answer:
The value of k in the equation (x - k)^2 = x^2 - 88x + k^2 is found by comparing coefficients, which yields k = 44.
Step-by-step explanation:
The student's question involves solving for the variable k from a given algebraic equation. The equation provided seems to suggest a typo, but implies to be (x - k)2 = x2 - 88x + k2, which after expanding and simplifying should yield a relationship between x and k. To solve for k, one would expand the left side to obtain x2 - 2kx + k2 and compare it to the right side of the equation. If the two expressions are equal for all x, then the corresponding coefficients must be equal. This means that -2k must be equal to -88 (the coefficient of x). Therefore, k can be found by dividing -88 by -2, which gives us k = 44.