We are given the equation $(x-A)^2 + B = x^2 - 10x + 29$ and asked to find the value of $A + B$.

1. Problem Description

We are given the equation $(x-A)^2 + B = x^2 - 10x + 29$ and asked to find the value of $A + B$.

2. Solution Steps

First, we expand the left side of the equation:

$(x-A)^2 + B = (x^2 - 2Ax + A^2) + B = x^2 - 2Ax + (A^2 + B)$.

We are given that $(x-A)^2 + B = x^2 - 10x + 29$.

Therefore, we have $x^2 - 2Ax + (A^2 + B) = x^2 - 10x + 29$.

Now we equate the coefficients of the corresponding terms.

Equating the $x$ terms, we have $-2A = -10$.

Dividing both sides by $-2$, we get $A = \frac{-10}{-2} = 5$.

Equating the constant terms, we have $A^2 + B = 29$.

Since we know $A = 5$, we substitute this into the equation:

$5^2 + B = 29$, which means $25 + B = 29$.

Subtracting $25$ from both sides, we get $B = 29 - 25 = 4$.

Now we can find $A + B = 5 + 4 = 9$.

3. Final Answer

$A+B=9$