To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints using algebraic terms.

Let's denote:
- $x_1$ as 'hours worked by Laura'
- $x_2$ as 'hours worked by Bobby'

The objective function is to minimize: 
\[3x_1^2 + 7x_1x_2 + 7x_2^2 + 4x_1\]

Constraints:
1. Laura's work quality rating is 5: $5x_1 = 5$ (However, this constraint seems to imply that the hours worked by Laura must be 1 to satisfy the equation as given. For clarity and assuming a misunderstanding in interpretation, we'll consider it as a requirement for her work quality rating per hour.)
2. Bobby's work quality rating is 2: $2x_2 = 2$ (Similar to Laura's, this implies hours worked by Bobby must be 1 if taken literally. We interpret these as ratings per hour of work.)
3. Total combined work quality rating from hours worked by Laura and Bobby is at least 25: $5x_1 + 2x_2 \geq 25$
4. (Duplicate of constraint 3, so we ignore it for simplicity)
5. Eight times the number of hours worked by Laura plus -10 times the number of hours worked by Bobby has to be at least zero: $8x_1 - 10x_2 \geq 0$
6. The total combined work quality rating from hours worked by Laura squared plus hours worked by Bobby squared must be 58 or less: $(5x_1)^2 + (2x_2)^2 \leq 58$

Given the clarification on variable definitions and constraints, we now have a symbolic representation of the problem:
```json
{
  'sym_variables': [('x1', 'hours worked by Laura'), ('x2', 'hours worked by Bobby')],
  'objective_function': '3*x1**2 + 7*x1*x2 + 7*x2**2 + 4*x1',
  'constraints': [
    '5*x1 + 2*x2 >= 25',
    '8*x1 - 10*x2 >= 0',
    '(5*x1)**2 + (2*x2)**2 <= 58'
  ]
}
```

Now, let's implement this in Gurobi:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x1 = m.addVar(name='hours_worked_by_Laura', lb=-GRB.INFINITY)
x2 = m.addVar(name='hours_worked_by_Bobby', lb=-GRB.INFINITY)

# Set the objective function
m.setObjective(3*x1**2 + 7*x1*x2 + 7*x2**2 + 4*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 2*x2 >= 25, name='total_work_quality')
m.addConstr(8*x1 - 10*x2 >= 0, name='hours_constraint')
m.addConstr((5*x1)**2 + (2*x2)**2 <= 58, name='quality_rating_squared')

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print('Optimal solution found:')
    print(f'Hours worked by Laura: {x1.x}')
    print(f'Hours worked by Bobby: {x2.x}')
else:
    print('No optimal solution found')
```