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Completing the Square Calculator

Completing the Square
\[ ax^2 + bx + c = 0 \]
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Calculator Use

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:

\( 2x^2 - 12x + 7 = 0 \)

\( a \ne 1, a = 2 \) so divide through by 2

\( \dfrac{2}{2}x^2 - \dfrac{12}{2}x + \dfrac{7}{2} = \dfrac{0}{2} \)

which gives us

\( x^2 - 6x + \dfrac{7}{2} = 0 \)

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:

\( x^2 + 0x - 4 = 0 \)

Eliminate b term with 0 to get:

\( x^2 - 4 = 0 \)

Keep \( x \) terms on the left and move the constant to the right side by adding it on both sides

\( x^2 = 4\)

Take the square root of both sides

\( x = \pm \sqrt[]{4} \)

therefore

\( x = + 2 \)
\( x = - 2 \)
 

Cite this content, page or calculator as:

Furey, Edward "Completing the Square Calculator"; from https://www.calculatorsoup.com - Online Calculator Resource.

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