Completing the Square Practice
Master solving quadratic equations with step-by-step practice problems and examples
Quadratic Equation Solver
Coefficient of x²
Coefficient of x
Constant term
Current Equation:
Solution
Completed Square Form
Additional Information
Discriminant (b² - 4ac): 0.000
Nature of roots: Real
Method: Completing the Square
Step-by-Step Solution
Given equation: 1x² +0x +0 = 0
Move constant to right side: x² +0.000x = 0.000
To complete the square, add (0.000/2)² = (0.000)² = 0.000 to both sides
x² +0.000x + 0.000 = 0.000
Factor left side: (x +0.000)² = 0.000
Take square root of both sides: x +0.000 = ±0.000
x = 0.000 + 0.000 = 0.000
x = 0.000 - 0.000 = 0.000
Completing the Square Formula
General Form
Steps
- 1. Divide by 'a' if a ≠ 1
- 2. Move constant to right side
- 3. Add (b/2)² to both sides
- 4. Factor left side as perfect square
- 5. Take square root of both sides
- 6. Solve for x
Mathematical Symbols
Tips & Tricks
Always check if the coefficient 'a' equals 1 first
The term to add is always (b/2)²
Negative discriminant means complex solutions
Perfect square trinomials have discriminant = 0
Understanding Completing the Square
What is Completing the Square?
Completing the square is a method for solving quadratic equations by transforming them into a perfect square trinomial. This technique is particularly useful when the quadratic doesn't factor easily.
Why Use This Method?
- •Works for any quadratic equation
- •Reveals the vertex form of a parabola
- •Foundation for deriving the quadratic formula
- •Useful in calculus and advanced mathematics
Step-by-Step Process
Step 1: Standard Form
Ensure equation is in ax² + bx + c = 0 form
Step 2: Normalize
Divide by 'a' to make coefficient of x² equal to 1
Step 3: Complete
Add (b/2)² to both sides of the equation
Step 4: Factor
Write left side as (x + b/2)²
Step 5: Solve
Take square root and solve for x
Example Problems
Example 1: Simple Case
x² + 8x - 9 = 0
Move constant: x² + 8x = 9
Complete square: x² + 8x + 16 = 9 + 16
Factor: (x + 4)² = 25
Solve: x + 4 = ±5
Solutions: x = 1 or x = -9
Example 2: Complex Solutions
x² - 8x + 20 = 0
Move constant: x² - 8x = -20
Complete square: x² - 8x + 16 = -20 + 16
Factor: (x - 4)² = -4
Solve: x - 4 = ±2i
Solutions: x = 4 ± 2i