Menu

Completing The Square In Quadratics Calculator

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 2 Votes ]

The Completing The Square In Quadratics Calculator will calculate and:

  1. Complete the square in a quadratic equation of the form ax2 + bx + c = 0.

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

Completing The Square In Quadratics Calculator
Completing The Square In Quadratics Calculator Results (detailed calculations and formula below)
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
a(x + b/2a)2 + (c - b2/4a2) = 0
(x + /2 × )2 + ( - 2/4 × 2) = 0
(x + /)2 + ( - /4 × ) = 0
(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.

We hope you found the Completing The Square In Quadratics Calculator useful, if you did, we kindly request that you rate this calculator and, if you have time, share to your favourite social network. This allows us to allocate future resource and keep these Math calculators and educational material free for all to use across the globe.

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 2 Votes ]
Completing The Square In Quadratics. This image shows the properties and completing the square in quadratics formula for the Completing The Square In Quadratics

Related Fields with Tutorials

  1. Engineering
  2. Physics

Theoretical description

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

y = ax2 + bx + c = 0

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

For example, the equation 3x2 - 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

ax2 + 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

ax2 + bx + c = a(x + p)2 + q
ax2 + bx + c = a(x2 + 2px + p2) + q
ax2 + bx + c = ax2 + 2apx + ap2 + q

Comparing the like terms on both sides yields

b = 2ap

Hence,

p = b/2a

and

c = ap2 + q

Thus,

q = c - ap2
= c - a ∙ (b/2a)2
= c - b2/4a2

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

a(x + b/2a)2 + (c - b2/4a2) = 0

For example, we can write the quadratic equation 3x2 - 4x + 1 = 0 (a = 3, b = -4 and c = 1) as

3(x + -4/2∙3)2 + (1 - -42/4 ∙ 32 ) = 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

Equations Math Tutorials associated with the Completing The Square In Quadratics Calculator

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.

Math Calculators

You may also find the following Math calculators useful.