Welcome to this Quadratic Calculator

This is a calculator to determine the solutions to Quadratic Equations in the form of ax² + bx + c = 0 using the Quadratic Formula or by Factoring if possible

Please enter your a, b, and c below:

a:    b:    c:   




What is the Quadratic Formula??


This formula comes from our initial format for a quadratic. We can use the technique completing the square to develop this formula.

  1.   ax² + bx + c = 0        This is our initial format
  2.   ax² + bx = –c        We first subtract c
  3.   x² + (b/a)x = -(c/a)        Then divide by a
  4.   x² + (b/a)x + (b²/4a²) = -(c/a) + (b²/4a²)        Complete the square
  5.   x² + (b/a)x + (b²/4a²) = (b²/4a²) - (4ac/4a²)        And make a common denominator
  6.   x² + (b/a)x + (b²/4a²) = (b² - 4ac)/4a²        Combine the fractions on the right
  7.   (x + (b/2a))² = (b² - 4ac)/4a²        Finish the square
  8.   x + (b/2a) = √(b² - 4ac)/2a        Take the square root
  9.   x = -b ± √(b² - 4ac)        And solve
  10. ━━━━━━━━━━━━━    
  11. 2a       
The Quadratic Formula