To find the value of z such that both 9 and -9 are solutions to the equation x² + z = 103, we start by substituting the values of x into the equation.
1. First, let’s substitute x = 9:
x² + z = 103
9² + z = 103
81 + z = 103
Now, we isolate z:
z = 103 – 81
z = 22
2. Now, let’s check by substituting x = -9:
x² + z = 103
(-9)² + z = 103
81 + z = 103
Again, it gives us:
z = 103 – 81
z = 22
Since both substitutions lead us to the same value of z = 22, we can conclude that the required value is:
z = 22