Solving Quadratic Equations by Completing the Square

Overview

• Previous videos covered:
  • Solving quadratic equations by factoring
  • Extracting square roots
• Today's focus: Completing the square method.

Example Equation

• Given:
  x² + 6x - 2 = 0

Steps to Solve by Completing the Square

1. Transposing the Constant:

   • Move the constant (-2) to the other side:
     x² + 6x = 2

2. Finding the Third Term:

   • To make a perfect square trinomial, add (b/2)²:
   • Here, b = 6.
   • Calculation:
     • 6 / 2 = 3
     • 3² = 9
   • Update the equation:
     x² + 6x + 9 = 2 + 9
   • Result:
     x² + 6x + 9 = 11

3. Express as a Square of a Binomial:

   • x² + 6x + 9 = (x + 3)²
   • Therefore:
     (x + 3)² = 11

4. Extracting Square Roots:

   • Take square roots of both sides:
     x + 3 = ±√11

5. Isolating x:

   • Transpose +3:
     x = ±√11 - 3
   • This gives two solutions:
     • x₁ = √11 - 3
     • x₂ = -√11 - 3

Conclusion

• The solutions for the equation x² + 6x - 2 = 0 are:
  • x₁ = -3 + √11
  • x₂ = -3 - √11
• Next video will explore cases where the coefficient of x² is greater than one.

Reminder

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