How to Solve Quadratic Equations by Completing the Square

 

When factoring is tough, completing the square is a great way to solve quadratic equations. Here’s an example.

Problem:
Solve $x^2 + 6x - 7 = 0$ by completing the square.

Solution:

1. Move the constant term:
   $x^2 + 6x = 7$
2. Add $9$ to both sides:
   $x^2 + 6x + 9 = 16$
3. Now, rewrite as a perfect square:
   $(x + 3)^2 = 16$
4. Take the square root of both sides:
   $x + 3 = \pm 4$
5. Solve for $x$:
   $x = 1$ or $x = -7$

Conclusion:
Completing the square is a useful method for solving quadratic equations that don’t factor easily.