Solve 2x² + 7x + 3 = 0

Step-by-step solution

1. Identify $a = 2$, $b = 7$, $c = 3$.

2. Compute $ac = 2 \cdot 3 = 6$. Find two numbers multiplying to $6$ and adding to $b = 7$: that's $1$ and $6$.

3. Split the middle term: $2x^2 + x + 6x + 3$.

4. Factor by grouping: $x(2x + 1) + 3(2x + 1) = (2x + 1)(x + 3)$.

5. Set each factor to zero: $x = -\tfrac{1}{2}$ or $x = -3$.