Completing the Square Calculator
This calculator is a quadratic equation solver that will solve a second-order polynomial equation in the form ax2 + bx + c = 0 for x, where a ≠ 0, using the completing the square method.
The calculator solution will show work to solve a quadratic equation by completing the square to solve the entered equation for real and complex roots.
Completing the square when a is not 1
To complete the square when a is greater than 1 or less than 1 but not equal to 0, factor out the value of a from all other terms.
For example, find the solution by completing the square for:
\( a \ne 1, a = 2 \) so divide through by 2
which gives us
Now, continue to solve this quadratic equation by completing the square method.
Completing the square when b = 0
When you do not have an x term because b is 0, you will have a easier equation to solve and only need to solve for the squared term.
For example: Solution by completing the square for:
Eliminate b term with 0 to get:
Keep \( x \) terms on the left and move the constant to the right side by adding it on both sides
Take the square root of both sides