Completing Square 2B6298

1. **Stating the problem:** We need to solve quadratic expressions or equations by completing the square. 2. **Formula and rules:** The general form of a quadratic is $$ax^2 + bx + c$$. To complete the square, we rewrite it as $$a(x-h)^2 + k$$ where $$h$$ and $$k$$ are constants. 3. **Step-by-step method:** - Divide the quadratic by $$a$$ if $$a \neq 1$$. - Move the constant term to the other side if solving an equation. - Take half of the coefficient of $$x$$, square it, and add it to both sides. - Use \cancel{} to show adding and subtracting the same value. - Factor the perfect square trinomial. 4. **Example:** Solve $$x^2 + 6x + 5 = 0$$ by completing the square. 5. Move constant: $$x^2 + 6x = -5$$ 6. Half of 6 is 3, square is 9. Add 9 to both sides: $$x^2 + 6x + \cancel{9} = -5 + \cancel{9}$$ 7. Factor left side: $$(x + 3)^2 = 4$$ 8. Take square root: $$x + 3 = \pm 2$$ 9. Solve for $$x$$: $$x = -3 \pm 2$$ 10. Final answers: $$x = -1$$ or $$x = -5$$