1. Start with the equation: $4x^2 + 4x - 3 = 0$.
2. Move the constant term to the other side: $4x^2 + 4x = 3$.
3. Divide all terms by the leading coefficient (4): $x^2 + x = \frac{3}{4}$.
4. Complete the square by adding $(\frac{1}{2})^2 = \frac{1}{4}$ to both sides: $x^2 + x + \frac{1}{4} = \frac{3}{4} + \frac{1}{4}$.
5. Simplify the right side: $x^2 + x + \frac{1}{4} = 1$.
6. Write the left side as a perfect square: $(x + \frac{1}{2})^2 = 1$.
7. Take the square root of both sides: $x + \frac{1}{2} = \pm 1$.
8. Solve for x: $x = -\frac{1}{2} \pm 1$.
9. Calculate the two solutions: $x = \frac{1}{2}$ and $x = -\frac{3}{2}$.
Parent Tip: Review the logic above to help your child master the concept of solving quadratic equations by completing the square worksheets.
