WEBVTT

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Pozdravljeni v videu o 
dopolnjevanju kvadratov.

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Kaj je dopolnjevanje kvadratov?

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Je eden od načinov 
reševanja kvadratnih enačb.

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Preden -- no, naj napišem
kvadratno enačbo

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nato pa bom pokazal,
kako dopolniti kvadrat.

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Pozneje bom naredili še en primer,
mogoče še enega, potem pa

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bomo povedali, zakaj to imenujemo
dopolnjevanje kvadratov.

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Imamo npr. naslednjo enačbo:
x na kvadrat plus 16x

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minus 57 je enako 0.

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Torej... ali že znamo kaj,
kar bi nam lahko pomagalo

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rešiti ta problem?

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Lahko poskusimo s faktorizacijo.

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Kateri dve števili seštejemo, 
da dobimo 16, in zmnožimo,

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da dobimo -57?

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Verjetno morate malo premisliti.

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Lahko bomo dobili cela
števila, vendar nismo niti

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prepričani, da obstajata
celi števili, ki data

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tak rezultat.

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V tem primeru obstajata.

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Ampak včasih je rešitev
decimalno število,

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pa tega ne vemo.

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Torej, faktorizacija je uporabna
samo, če smo prepričani,

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da lahko najdemo primerna
cela števila.

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Se pravi, x plus celo število
ali x minus celo število

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krat x plus neko celo število.

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Ali nekaj podobnega.

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Druga možnost je reševanje
kvadratne enačbe.

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Videli bomo, da 
je kvadratna enačba

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samo bližnjica do dopolnitve kvadratov.

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Kvadratno enačbo 
celo dokažemo z dopolnitvijo

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kvadrata.

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Kaj je torej dopolnitev kvadrata?

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Kaj naredimo?

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