14-3xx=-x+4 eching

$$14 - 3 x x = - x + 4$$

x uchun yechish

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1,666666667$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$14-3x^{2}=-x+4$$

x ni ikki tarafga qo’shing.

$$14-3x^{2}+x=4$$

Ikkala tarafdan 4 ni ayirish.

$$14-3x^{2}+x-4=0$$

10 olish uchun 14 dan 4 ni ayirish.

$$10-3x^{2}+x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-3x^{2}+x+10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 1 ni b va 10 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-3\right)\times 10}}{2\left(-3\right)}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-3\right)\times 10}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+12\times 10}}{2\left(-3\right)}$$

12 ni 10 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+120}}{2\left(-3\right)}$$

1 ni 120 ga qo'shish.

$$x=\frac{-1±\sqrt{121}}{2\left(-3\right)}$$

121 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±11}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-1±11}{-6}$$

x=\frac{-1±11}{-6} tenglamasini yeching, bunda ± musbat. -1 ni 11 ga qo'shish.

$$x=\frac{10}{-6}$$

\frac{10}{-6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{5}{3}$$

x=\frac{-1±11}{-6} tenglamasini yeching, bunda ± manfiy. -1 dan 11 ni ayirish.

$$x=-\frac{12}{-6}$$

-12 ni -6 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=-\frac{5}{3} x=2$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$14-3x^{2}=-x+4$$

x ni ikki tarafga qo’shing.

$$14-3x^{2}+x=4$$

Ikkala tarafdan 14 ni ayirish.

$$-3x^{2}+x=4-14$$

-10 olish uchun 4 dan 14 ni ayirish.

$$-3x^{2}+x=-10$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}+x}{-3}=-\frac{10}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1}{-3}x=-\frac{10}{-3}$$

1 ni -3 ga bo'lish.

$$x^{2}-\frac{1}{3}x=-\frac{10}{-3}$$

-10 ni -3 ga bo'lish.

$$x^{2}-\frac{1}{3}x=\frac{10}{3}$$

-\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{6} olish uchun. Keyin, -\frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{3}x+\left(-\frac{1}{6}\right)^{2}=\frac{10}{3}+\left(-\frac{1}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{6} kvadratini chiqarish.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{10}{3}+\frac{1}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{10}{3} ni \frac{1}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{121}{36}$$

x^{2}-\frac{1}{3}x+\frac{1}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{121}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{121}{36}}$$

Qisqartirish.

$$x-\frac{1}{6}=\frac{11}{6} x-\frac{1}{6}=-\frac{11}{6}$$

\frac{1}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=2 x=-\frac{5}{3}$$