-3x^2=-11x+12 eching

$$- 3 x ^ { 2 } = - 11 x + 12$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{23}i+11}{6}\approx 1,833333333-0,799305254i$$

$$x=\frac{11+\sqrt{23}i}{6}\approx 1,833333333+0,799305254i$$

Kvadrat tenglamalaridan foydalanish qoidalari

11x ni ikki tarafga qo’shing.

$$-3x^{2}+11x=12$$

Ikkala tarafdan 12 ni ayirish.

$$-3x^{2}+11x-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 11 ni b va -12 ni c bilan almashtiring.

$$x=\frac{-11±\sqrt{11^{2}-4\left(-3\right)\left(-12\right)}}{2\left(-3\right)}$$

11 kvadratini chiqarish.

$$x=\frac{-11±\sqrt{121-4\left(-3\right)\left(-12\right)}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121+12\left(-12\right)}}{2\left(-3\right)}$$

12 ni -12 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121-144}}{2\left(-3\right)}$$

121 ni -144 ga qo'shish.

$$x=\frac{-11±\sqrt{-23}}{2\left(-3\right)}$$

-23 ning kvadrat ildizini chiqarish.

$$x=\frac{-11±\sqrt{23}i}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{23}i}{-6}$$

x=\frac{-11±\sqrt{23}i}{-6} tenglamasini yeching, bunda ± musbat. -11 ni i\sqrt{23} ga qo'shish.

$$x=\frac{-11+\sqrt{23}i}{-6}$$

-11+i\sqrt{23} ni -6 ga bo'lish.

$$x=\frac{-\sqrt{23}i+11}{6}$$

x=\frac{-11±\sqrt{23}i}{-6} tenglamasini yeching, bunda ± manfiy. -11 dan i\sqrt{23} ni ayirish.

$$x=\frac{-\sqrt{23}i-11}{-6}$$

-11-i\sqrt{23} ni -6 ga bo'lish.

$$x=\frac{11+\sqrt{23}i}{6}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{23}i+11}{6} x=\frac{11+\sqrt{23}i}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

11x ni ikki tarafga qo’shing.

$$-3x^{2}+11x=12$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}+11x}{-3}=\frac{12}{-3}$$

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

$$x^{2}+\frac{11}{-3}x=\frac{12}{-3}$$

11 ni -3 ga bo'lish.

$$x^{2}-\frac{11}{3}x=\frac{12}{-3}$$

12 ni -3 ga bo'lish.

$$x^{2}-\frac{11}{3}x=-4$$

-\frac{11}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{11}{6} olish uchun. Keyin, -\frac{11}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{11}{3}x+\left(-\frac{11}{6}\right)^{2}=-4+\left(-\frac{11}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{6} kvadratini chiqarish.

$$x^{2}-\frac{11}{3}x+\frac{121}{36}=-4+\frac{121}{36}$$

-4 ni \frac{121}{36} ga qo'shish.

$$x^{2}-\frac{11}{3}x+\frac{121}{36}=-\frac{23}{36}$$

x^{2}-\frac{11}{3}x+\frac{121}{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.

$$\left(x-\frac{11}{6}\right)^{2}=-\frac{23}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{11}{6}\right)^{2}}=\sqrt{-\frac{23}{36}}$$

Qisqartirish.

$$x-\frac{11}{6}=\frac{\sqrt{23}i}{6} x-\frac{11}{6}=-\frac{\sqrt{23}i}{6}$$

\frac{11}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{11+\sqrt{23}i}{6} x=\frac{-\sqrt{23}i+11}{6}$$