## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hydrangeas' and 'aloe vera', which we can denote as $x_1$ and $x_2$ respectively. The objective function to minimize is $1 \cdot x_1^2 + 5x_1 + 9x_2$. The constraints are:
- $3x_1 + 26x_2 \geq 52$
- $3x_1 + 26x_2 \geq 52$ (same as the previous one, so we keep it as is)
- $27x_1 + 19x_2 \geq 45$
- $-8x_1^2 + 5x_2^2 \geq 0$
- $3x_1 + 26x_2 \leq 120$
- $27^2x_1^2 + 19^2x_2^2 \leq 172^2$ is incorrect based on the problem statement, it should be $x_1^2 + x_2^2 \leq 172$ or more accurately interpreted as $27x_1 + 19x_2 \leq 172$ for cost, but given $x_1^2 + x_2^2$ does not directly match any statement, we focus on given constraints.
- $x_1$ and $x_2$ are non-negative integers.

## 2: Correct and clarify constraints based on the problem statement
Correcting and clarifying:
- The resilience index constraint is $3x_1 + 26x_2 \geq 52$ and $3x_1 + 26x_2 \leq 120$.
- The cost constraint is $27x_1 + 19x_2 \geq 45$ and $27x_1 + 19x_2 \leq 172$.

## 3: Formulate the symbolic representation
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'hydrangeas'), ('x2', 'aloe vera')],
'objective_function': '1*x1^2 + 5*x1 + 9*x2',
'constraints': [
    '3*x1 + 26*x2 >= 52',
    '27*x1 + 19*x2 >= 45',
    '-8*x1^2 + 5*x2^2 >= 0',
    '3*x1 + 26*x2 <= 120',
    '27*x1 + 19*x2 <= 172',
    'x1 >= 0 and x1 is an integer',
    'x2 >= 0 and x2 is an integer'
]
}
```

## 4: Convert to Gurobi Python code
```python
import gurobi

def optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(name="hydrangeas", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="aloe_vera", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(1*x1**2 + 5*x1 + 9*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(3*x1 + 26*x2 >= 52, name="resilience_index_min")
    model.addConstr(27*x1 + 19*x2 >= 45, name="cost_min")
    model.addConstr(-8*x1**2 + 5*x2**2 >= 0, name="non_linear_constraint")
    model.addConstr(3*x1 + 26*x2 <= 120, name="resilience_index_max")
    model.addConstr(27*x1 + 19*x2 <= 172, name="cost_max")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hydrangeas: {x1.varValue}")
        print(f"Aloe Vera: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```

The final answer is: 
```python
import gurobi

def optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(name="hydrangeas", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="aloe_vera", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(1*x1**2 + 5*x1 + 9*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(3*x1 + 26*x2 >= 52, name="resilience_index_min")
    model.addConstr(27*x1 + 19*x2 >= 45, name="cost_min")
    model.addConstr(-8*x1**2 + 5*x2**2 >= 0, name="non_linear_constraint")
    model.addConstr(3*x1 + 26*x2 <= 120, name="resilience_index_max")
    model.addConstr(27*x1 + 19*x2 <= 172, name="cost_max")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hydrangeas: {x1.varValue}")
        print(f"Aloe Vera: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```