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Completing The Square In Quadratics Calculator

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.

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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

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