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

You would use this calculator to sole a quadratic equation. This calculator (using the completing the square method) will solve a second-order polynomial equation in the form $ax^2 + bx + c = 0$ for x, where $a ≠ 0$.

Enter value of both operand $x$

**$ a = $**

**$ b = $**

**$ c = $**

Examples

#### 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

- $x^2 + 0x - 16 = 0$
**Get rid of b term with 0:**

$x^2 - 16 = 0 $**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 $**Take the square root of both sides**

$x = ± √16 $**we get,**

$x = ±4 $**thus,**

$x = +4 $

$x = -4 $

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

When

- $3x^2 - 36x + 42 = 0$
**$a ≠ 1$, $a = 3$, we will divide through all parts of the equation by 3**

$(3x^2)/3 - (36x)/3 + 42/3 = 0/3 $**Which gives us**

$x^2 - 12x + 14 = 0 $**Let's continue to solve this by completing the square method**

$x^2 - 12x = -14 $**Add 36, completing the square**

$x^2 - 12x + 36 = -14 + 36 $**Which gives us**

$(x-6)^2 = 22 $**Which gives us**

$√(x-6)^2 = ± √22 $**Which gives us**

$x = ± √22 + 6 $**thus,**

$x = + √22 + 6 $

$x = - √22 + 6 $