Completing the Square Calculator ( $\;ax^2 + bx +c \; = 0$ )

Completing the square for $b = 0$

When you don't have x term i.e. $b=0$, this becomes rather straightforward to solve the quadratic equation. Let's assume this example solution to complete the square for

1. $x^2 + 0x - 16 = 0$
2. Get rid of b term with 0:
   $x^2 - 16 = 0 $
3. Keep x terms on the left side of the equation and move the constant to the right side. We can do this by adding the number on both sides of the equation.
   $x^2 = 16 $
4. Take the square root of both sides
   $x = ± √16 $
5. we get,
   $x = ±4 $
6. thus,
   $x = +4 $
   $x = -4 $
   

Completing the square for $a ≠ 1$ and $a ≠ 0$

When

1. $3x^2 - 36x + 42 = 0$
2. $a ≠ 1$, $a = 3$, we will divide through all parts of the equation by 3
   $(3x^2)/3 - (36x)/3 + 42/3 = 0/3 $
3. Which gives us
   $x^2 - 12x + 14 = 0 $
4. Let's continue to solve this by completing the square method
   $x^2 - 12x = -14 $
5. Add 36, completing the square
   $x^2 - 12x + 36 = -14 + 36 $
6. Which gives us
   $(x-6)^2 = 22 $
7. Which gives us
   $√(x-6)^2 = ± √22 $
8. Which gives us
   $x = ± √22 + 6 $
9. thus,
   $x = + √22 + 6 $
   $x = - √22 + 6 $