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From Wikipedia, the free encyclopedia
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Animation depicting the process of completing the square. ( Details , animated GIF version )

In elementary algebra , completing the square is a technique for converting a Altuzarra RuffleTrimmed KneeLength Skirt Best Place To Buy Online OSPbQHEJ
of the form

to the form

for some values of h and k .

Completing the square is used in

In mathematics, completing the square is often applied in any computation involving quadratic polynomials. Completing the square is also used to derive the quadratic formula .

Contents

There is a simple formula in elementary algebra for computing the Balenciaga Long Sleeve KneeLength Coat Websites Online TrMJ7miH
of a binomial :

For example:

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of x is twice the number p , and the Ulla Johnson KneeLength Sleeveless Dress Cheap Best Sale BCr1T2JgR
is equal to p 2 .

Consider the following quadratic Clearance Comfortable The Cast 2 Skinnyfit Distressed Denim Jeans Mid denim John Elliott Co Clearance Sneakernews Xsa8PqaB
:

This quadratic is not a perfect square, since 28 is not the square of 5:

However, it is possible to write the original quadratic as the sum of this square and a constant:

This is called completing the square .

Given any monic quadratic

it is possible to form a square that has the same first two terms:

This square differs from the original quadratic only in the value of the constant term. Therefore, we can write

where k = c b 2 4 {\displaystyle k\,=\,c-{\frac {b^{2}}{4}}} . This operation is known as completing the square . For example:

Given a quadratic polynomial of the form

it is possible to factor out the coefficient a , and then complete the square for the resulting striped gathered shirt Blue Damir Doma Discount Cheap In China For Sale Clearance Official Site Cheap Websites Cheap Sale Cheapest XTAAHk
.

Example:

This allows us to write any quadratic polynomial in the form

The result of completing the square may be written as a formula. For the general case: [1]

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Synonyms

Sentences Sentence examples

, in North Carolina the governor has no veto power.
He was cold and tired, and, , he was hungry.
, this belief that prophecy had ceased led the religious personalities of the later time to authenticate their message by means of antedated prophecy.
, with the large furnaces which gas-firing makes possible mechanical appliances may be substituted for manual labour in many operations, such as removing and replacing broken retorts, mixing and conveying the charge, drawing and casting the metal, charging and emptying the retorts, and removing the residues and products.
This house is on the best street in the neighborhood; , it has easy access to the highway.
The team was having a great season and, , all the players were getting along.
This college has a great reputation and, , you’ll be close to the city so we can visit easily.
I don’t know what happened at the party last night and, , I don’t want to know.
, the observations on American wasps render it probable that the earlier accounts of the instinctive behaviour of such wasps are exaggerated.
Thus the cardinal number of a is itself a class, and a is a member of it.
, apart from the gradual disintegration of the empire, Athens was disturbed by political strife.
We thus see how the power of the house of Omayya developed itself, and how there arose against it an opposition, which led in the first place to the murder of Othman and the Caliphate of Ali, and , during the whole period of the Omayyad caliphs, repeatedly to dangerous outbreaks, culminating in the great catastrophe which placed the Abbasids on the throne.
, the governmental machinery would be less complex than in the older towns.
, the fact that the Syriac Sen'ar = Shinar was later used to denote the region about Bagdad (northern Babylonia) does not necessarily prove that Shinar-Shumer meant only northern Babylonia, because, when the term Sen'ar was applied to the Bagdad district the great southern Babylonian civilization had long been forgotten and " Babylonia " really meant only what we now know as northern Babylonia.
It was charged that he was in contempt of the Senate in having failed to submit on request a complete report of the management of his office.
, Congress in 1902 appropriated the receipts from the sales of public lands in the state to the construction of irrigation work.
, the Boghaz Keui tablets, though only partially deciphered as yet, go far to settle the question.
, he was a man of great ambition, persuasive eloquence and wide generosity; qualities which especially appealed at that time to the classes from whom he was to draw his support.
we find that (probably after the Persian War) the office is thrown open to the second class, and finally in 457 B.C. we meet an archon, Mnesitheides, of the third, or Zeugite, class.
, the relations between the Philippians and himself presuppose, on any fair estimate, an interval of time which cannot be crushed into a few months.
, the organization of ecclesiastical offices remained unchanged: the division of the Church into bishoprics and the grouping together of bishoprics into metropolitan dioceses.
This passage offers important corroboration of the Icelandic accounts of the Vinland voyages, and is, , interesting "as the only undoubted reference to Vinland in a medieval book written beyond the limits of the Scandinavian world" (Fiske).
it is not till 457 that even a Zeugite archon is known, according to the Constitution of Athens (c. 26), which dates the change as five years after the death of Ephialtes and does not connect it with Aristides.
, Gyllenskold says that when arcs mounted, as they not infrequently did, from the horizon, their apparent width might go on increasing right up to the zenith, or it might increase until an altitude of about 45° was reached and then diminish, appearing much reduced when the zenith was reached.
, agriculture is everywhere accompanied on the sand-grounds by the rearing of sheep and cattle, which assist in fertilizing the soil.
, in order to encourage the growth and preservation of the forests, and to create systematically forest reserves, the legislature established in 1899 a State Forestry Board.
, the visionary who is found at most periods of great spiritual excitement was forced by the prejudice of his time, which refused to acknowledge any inspiration in the present, to ascribe his visionary experiences and reinterpretations of the mysterious traditions of his people to some heroic figure of the past.
, the manufacturing schedule presupposes some uniformity in the method of accounting among different companies or lines of business, and this is often lacking.
he warned Athens against the treason of the extreme oligarchs, and induced the troops to raze a mole erected to facilitate a Spartan descent on Peiraeus.

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