To find the x coordinates of the solutions, we need to solve the system of equations:
1. x² + y² = 36 (Equation of a circle with radius 6 centered at the origin)
2. y = x + 6 (Equation of a line)
First, we can substitute the second equation into the first. Replace y in the first equation:
x² + (x + 6)² = 36
Now, expand the equation:
x² + (x² + 12x + 36) = 36
Combine like terms:
2x² + 12x + 36 = 36
Subtract 36 from both sides:
2x² + 12x = 0
Factor out 2x:
2x(x + 6) = 0
This gives us two solutions:
x = 0 and x + 6 = 0, which means x = -6.
Therefore, the x coordinates of the solutions are:
x = 0 and x = -6.