What is the sum of the two solutions of the equation `x^(2)-7x+3=0`?

Answer

To find the sum of the two solutions of the quadratic equation \(x^2 - 7x + 3 = 0\), we can use the relationship between the coefficients of the quadratic equation and its roots.

### Step-by-step Solution:

1. **Identify the coefficients**:
The given quadratic equation is in the standard form \(ax^2 + bx + c = 0\). Here, we identify:
- \(a = 1\) (coefficient of \(x^2\))
- \(b = -7\) (coefficient of \(x\))
- \(c = 3\) (constant term)

2. **Use the formula for the sum of the roots**:
The sum of the solutions (roots) of a quadratic equation can be calculated using the formula:
\[ x_1 + x_2 = -\frac{b}{a} \]
where \(x_1\) and \(x_2\) are the roots of the equation.

3. **Substitute the values of \(b\) and \(a\)**:
Plugging in the values we identified:
\[ x_1 + x_2 = -\frac{-7}{1} \]

4. **Simplify the expression**:
\[ x_1 + x_2 = \frac{7}{1} = 7 \]

5. **Conclusion**:
The sum of the two solutions of the equation \(x^2 - 7x + 3 = 0\) is \(7\).