4x^2/2-33x/3+14/6=0 eching

$$\frac { 4 x ^ { 2 } } { 2 } - \frac { 33 x } { 3 } + \frac { 14 } { 6 } = 0$$

x uchun yechish

$$x=\frac{\sqrt{921}}{12}+\frac{11}{4}\approx 5,278998484$$

$$x=-\frac{\sqrt{921}}{12}+\frac{11}{4}\approx 0,221001516$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 6 ga, 2,3,6 ning eng kichik karralisiga ko‘paytiring.

$$3\times 4x^{2}-2\times 33x+14=0$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$12x^{2}-2\times 33x+14=0$$

-66 hosil qilish uchun -2 va 33 ni ko'paytirish.

$$12x^{2}-66x+14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 12 ni a, -66 ni b va 14 ni c bilan almashtiring.

$$x=\frac{-\left(-66\right)±\sqrt{\left(-66\right)^{2}-4\times 12\times 14}}{2\times 12}$$

-66 kvadratini chiqarish.

$$x=\frac{-\left(-66\right)±\sqrt{4356-4\times 12\times 14}}{2\times 12}$$

-4 ni 12 marotabaga ko'paytirish.

$$x=\frac{-\left(-66\right)±\sqrt{4356-48\times 14}}{2\times 12}$$

-48 ni 14 marotabaga ko'paytirish.

$$x=\frac{-\left(-66\right)±\sqrt{4356-672}}{2\times 12}$$

4356 ni -672 ga qo'shish.

$$x=\frac{-\left(-66\right)±\sqrt{3684}}{2\times 12}$$

3684 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-66\right)±2\sqrt{921}}{2\times 12}$$

-66 ning teskarisi 66 ga teng.

$$x=\frac{66±2\sqrt{921}}{2\times 12}$$

2 ni 12 marotabaga ko'paytirish.

$$x=\frac{66±2\sqrt{921}}{24}$$

x=\frac{66±2\sqrt{921}}{24} tenglamasini yeching, bunda ± musbat. 66 ni 2\sqrt{921} ga qo'shish.

$$x=\frac{2\sqrt{921}+66}{24}$$

66+2\sqrt{921} ni 24 ga bo'lish.

$$x=\frac{\sqrt{921}}{12}+\frac{11}{4}$$

x=\frac{66±2\sqrt{921}}{24} tenglamasini yeching, bunda ± manfiy. 66 dan 2\sqrt{921} ni ayirish.

$$x=\frac{66-2\sqrt{921}}{24}$$

66-2\sqrt{921} ni 24 ga bo'lish.

$$x=-\frac{\sqrt{921}}{12}+\frac{11}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{921}}{12}+\frac{11}{4} x=-\frac{\sqrt{921}}{12}+\frac{11}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 6 ga, 2,3,6 ning eng kichik karralisiga ko‘paytiring.

$$3\times 4x^{2}-2\times 33x+14=0$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$12x^{2}-2\times 33x+14=0$$

-66 hosil qilish uchun -2 va 33 ni ko'paytirish.

$$12x^{2}-66x+14=0$$

Ikkala tarafdan 14 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$12x^{2}-66x=-14$$

Ikki tarafini 12 ga bo‘ling.

$$\frac{12x^{2}-66x}{12}=-\frac{14}{12}$$

12 ga bo'lish 12 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{66}{12}\right)x=-\frac{14}{12}$$

\frac{-66}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{11}{2}x=-\frac{14}{12}$$

\frac{-14}{12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{11}{2}x=-\frac{7}{6}$$

-\frac{11}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{11}{4} olish uchun. Keyin, -\frac{11}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{11}{2}x+\left(-\frac{11}{4}\right)^{2}=-\frac{7}{6}+\left(-\frac{11}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{4} kvadratini chiqarish.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=-\frac{7}{6}+\frac{121}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{7}{6} ni \frac{121}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=\frac{307}{48}$$

x^{2}-\frac{11}{2}x+\frac{121}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{11}{4}\right)^{2}=\frac{307}{48}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{11}{4}\right)^{2}}=\sqrt{\frac{307}{48}}$$

Qisqartirish.

$$x-\frac{11}{4}=\frac{\sqrt{921}}{12} x-\frac{11}{4}=-\frac{\sqrt{921}}{12}$$

\frac{11}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{921}}{12}+\frac{11}{4} x=-\frac{\sqrt{921}}{12}+\frac{11}{4}$$