1. Stating the problem: We are given the equation $$(x+a)^2 = x^2 + 22x + b$$ and need to find the values of $a$ and $b$. 2. Use the formula for expanding a binomial square: $$(x+a)^2 = x^2 + 2ax + a^2$$ 3. Compare the expanded form to the right side of the equation: $$x^2 + 2ax + a^2 = x^2 + 22x + b$$ 4. Equate the coefficients of like terms: - Coefficient of $x$: $$2a = 22$$ - Constant term: $$a^2 = b$$ 5. Solve for $a$: $$2a = 22$$ $$a = \frac{22}{2}$$ $$a = 11$$ 6. Find $b$ using $a^2$: $$b = a^2 = 11^2 = 121$$ Final answer: $$a = 11, b = 121$$