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
Cite this content, page or calculator as:
Furey, Edward "Completing the Square Calculator" at https://www.calculatorsoup.com/calculators/algebra/completing-the-square-calculator.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators