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3w^{2}+15w+12-w=0
Ikkala tarafdan w ni ayirish.
3w^{2}+14w+12=0
14w ni olish uchun 15w va -w ni birlashtirish.
w=\frac{-14±\sqrt{14^{2}-4\times 3\times 12}}{2\times 3}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 14 ni b va 12 ni c bilan almashtiring.
w=\frac{-14±\sqrt{196-4\times 3\times 12}}{2\times 3}
14 kvadratini chiqarish.
w=\frac{-14±\sqrt{196-12\times 12}}{2\times 3}
-4 ni 3 marotabaga ko'paytirish.
w=\frac{-14±\sqrt{196-144}}{2\times 3}
-12 ni 12 marotabaga ko'paytirish.
w=\frac{-14±\sqrt{52}}{2\times 3}
196 ni -144 ga qo'shish.
w=\frac{-14±2\sqrt{13}}{2\times 3}
52 ning kvadrat ildizini chiqarish.
w=\frac{-14±2\sqrt{13}}{6}
2 ni 3 marotabaga ko'paytirish.
w=\frac{2\sqrt{13}-14}{6}
w=\frac{-14±2\sqrt{13}}{6} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{13} ga qo'shish.
w=\frac{\sqrt{13}-7}{3}
-14+2\sqrt{13} ni 6 ga bo'lish.
w=\frac{-2\sqrt{13}-14}{6}
w=\frac{-14±2\sqrt{13}}{6} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{13} ni ayirish.
w=\frac{-\sqrt{13}-7}{3}
-14-2\sqrt{13} ni 6 ga bo'lish.
w=\frac{\sqrt{13}-7}{3} w=\frac{-\sqrt{13}-7}{3}
Tenglama yechildi.
3w^{2}+15w+12-w=0
Ikkala tarafdan w ni ayirish.
3w^{2}+14w+12=0
14w ni olish uchun 15w va -w ni birlashtirish.
3w^{2}+14w=-12
Ikkala tarafdan 12 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.
\frac{3w^{2}+14w}{3}=-\frac{12}{3}
Ikki tarafini 3 ga bo‘ling.
w^{2}+\frac{14}{3}w=-\frac{12}{3}
3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.
w^{2}+\frac{14}{3}w=-4
-12 ni 3 ga bo'lish.
w^{2}+\frac{14}{3}w+\left(\frac{7}{3}\right)^{2}=-4+\left(\frac{7}{3}\right)^{2}
\frac{14}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{3} olish uchun. Keyin, \frac{7}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
w^{2}+\frac{14}{3}w+\frac{49}{9}=-4+\frac{49}{9}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{3} kvadratini chiqarish.
w^{2}+\frac{14}{3}w+\frac{49}{9}=\frac{13}{9}
-4 ni \frac{49}{9} ga qo'shish.
\left(w+\frac{7}{3}\right)^{2}=\frac{13}{9}
w^{2}+\frac{14}{3}w+\frac{49}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(w+\frac{7}{3}\right)^{2}}=\sqrt{\frac{13}{9}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
w+\frac{7}{3}=\frac{\sqrt{13}}{3} w+\frac{7}{3}=-\frac{\sqrt{13}}{3}
Qisqartirish.
w=\frac{\sqrt{13}-7}{3} w=\frac{-\sqrt{13}-7}{3}
Tenglamaning ikkala tarafidan \frac{7}{3} ni ayirish.