1. **Problem Statement:** Solve the quadratic equation by middle term breaking. 2. **General Formula:** A quadratic equation is of the form $$ax^2 + bx + c = 0$$. 3. **Middle Term Breaking Method:** Find two numbers that multiply to $$a \times c$$ and add to $$b$$. 4. **Step-by-step:** - Split the middle term $$bx$$ into two terms using the two numbers found. - Factor by grouping. - Solve for $$x$$ by setting each factor equal to zero. 5. **Example:** Suppose the equation is $$x^2 + 5x + 6 = 0$$. - Here, $$a=1$$, $$b=5$$, $$c=6$$. - Find two numbers that multiply to $$1 \times 6 = 6$$ and add to $$5$$: these are $$2$$ and $$3$$. - Rewrite as $$x^2 + 2x + 3x + 6 = 0$$. - Group: $$(x^2 + 2x) + (3x + 6) = 0$$. - Factor each group: $$x(x + 2) + 3(x + 2) = 0$$. - Factor out common binomial: $$(x + 3)(x + 2) = 0$$. - Set each factor to zero: $$x + 3 = 0$$ or $$x + 2 = 0$$. - Solutions: $$x = -3$$ or $$x = -2$$. 6. **Final Answer:** $$x = -3$$ or $$x = -2$$.