To find the value of a in the equation 8z + 9 = 8z + 9 + a^2 + b, we need to first simplify the equation and isolate a.
Let’s start by simplifying both sides:
- The left-hand side (LHS):
8z + 9 - The right-hand side (RHS):
8z + 9 + a^2 + b
Notice that both sides have the same expression 8z + 9. We can subtract this expression from both sides:
8z + 9 - (8z + 9) = 8z + 9 + a^2 + b - (8z + 9)
Which simplifies to:
0 = a^2 + b
This result tells us that the sum of a squared and b must equal zero. For a square term like a^2 to be zero, a must be zero itself because the square of any real number is non-negative. Therefore:
a^2 = 0
From this equation, it follows that:
a = 0
Thus, the value of a is 0. The value of b must also be 0 for the equation to hold true.