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The Completing The Square In Quadratics Calculator will calculate and:

- Complete the square in a quadratic equation of the form ax
^{2}+ bx + c = 0.

**Completing The Square In Quadratics Calculator Parameters:** The quadratic equation is assumed to have two distinct roots.

Writing a quadratic equation in the form that shows the completing of the square:(x )^{2} + = 0 |

Completing the Square in Quadratics Formula and Calculations |
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a(x + )b/2a^{2} + (c - ) = 0b^{2}/4a^{2}(x + )/2 × ^{2} + ( - ) = 0^{2}/4 × ^{2}(x + )/^{2} + ( - ) = 0/4 × (x + )^{2} + ( - /) = 0/(x + )^{2} + () = 0/(x )^{2} + = 0 |

Completing The Square In Quadratics Calculator Input Values |

Coefficient a (a) = |

Coefficient b (b) = |

Constant c (c) = |

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each completing the square in quadratics calculation, the Completing The Square In Quadratics Calculator will automatically calculate the results and update the formula elements with each element of the completing the square in quadratics calculation. You can then email or print this completing the square in quadratics calculation as required for later use.

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A quadratic equation is a second-order equation with one variable of the form

y = ax^{2} + bx + c = 0

where x is the variable, a and b are coefficients and c is a constant.

For example, the equation 3x^{2} - 4x + 1 = 0 is a quadratic equation, where a = 3, b = -4 and c = 1.

A quadratic equation may have one or two roots or it may not have any root. One of the methods used for solving quadratic equations when they have two roots consists of completing the square. We must therefore try to express a given quadratic equation

ax^{2} + bx + c = 0

in the form

a(x+p)^{2} + q = 0

where p and q are numbers.

Let's write p and q in terms of the (known) coefficients a and b and the constant c. We have

ax^{2} + bx + c = a(x + p)^{2} + q

ax^{2} + bx + c = a(x^{2} + 2px + p^{2}) + q

ax^{2} + bx + c = ax^{2} + 2apx + ap^{2} + q

ax

ax

Comparing the like terms on both sides yields

b = 2ap

Hence,

p = *b**/**2a*

and

c = ap^{2} + q

Thus,

q = c - ap^{2}

= c - a ∙ (*b**/**2a*)^{2}

= c -*b*^{2}*/**4a*^{2}

= c - a ∙ (

= c -

Hence, we complete the square by writing the quadratic equation as

a(x + *b**/**2a*)^{2} + (c - *b*^{2}*/**4a*^{2}) = 0

For example, we can write the quadratic equation 3x^{2} - 4x + 1 = 0 (a = 3, b = -4 and c = 1) as

3(x + *-4**/**2∙3*)^{2} + (1 - *-4*^{2}*/**4 ∙ 3*^{2} ) = 0

3(x +*-4**/**6*)^{2} + (1 - *16**/**36*) = 0

3(x -*2**/**3*)^{2} + (*36**/**36* - *16**/**36*) = 0

3(x -*2**/**3*)^{2} + *20**/**36* = 0

3(x -*2**/**3*)^{2} + *5**/**9* = 0

3(x +

3(x -

3(x -

3(x -

The following Math tutorials are provided within the Equations section of our Free Math Tutorials. Each Equations tutorial includes detailed Equations formula and example of how to calculate and resolve specific Equations questions and problems. At the end of each Equations tutorial you will find Equations revision questions with a hidden answer that reveal when clicked. This allows you to learn about Equations and test your knowledge of Math by answering the revision questions on Equations.

- 9.1 - Variables, Coefficients and Constants. First Order Equations with One Variable
- 9.2 - Word Problems Involving Equations
- 9.3 - Identities
- 9.4 - Iterative Methods for Solving Equations
- 9.5 - Quadratic Equations
- 9.6 - The Quadratic Formula
- 9.7 - Systems of Linear Equations. Methods for Solving Them.
- 9.8 - Relationship between Equations in Linear Systems. Systems of Equations with One Linear and One Quadratic Equation