# 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

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 \$