(2x-1)(-3x+4)=-6x+11x+4 eching

$$( 2 x - 1 ) ( - 3 x + 4 ) = - 6 x + 11 x + 4$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{39}i}{6}+\frac{1}{2}\approx 0,5+1,040833i$$

$$x=-\frac{\sqrt{39}i}{6}+\frac{1}{2}\approx 0,5-1,040833i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x-1 ga -3x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-6x^{2}+11x-4=-6x+11x+4$$

5x ni olish uchun -6x va 11x ni birlashtirish.

$$-6x^{2}+11x-4=5x+4$$

Ikkala tarafdan 5x ni ayirish.

$$-6x^{2}+11x-4-5x=4$$

6x ni olish uchun 11x va -5x ni birlashtirish.

$$-6x^{2}+6x-4=4$$

Ikkala tarafdan 4 ni ayirish.

$$-6x^{2}+6x-4-4=0$$

-8 olish uchun -4 dan 4 ni ayirish.

$$-6x^{2}+6x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -6 ni a, 6 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-6\right)\left(-8\right)}}{2\left(-6\right)}$$

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\left(-6\right)\left(-8\right)}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+24\left(-8\right)}}{2\left(-6\right)}$$

24 ni -8 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-192}}{2\left(-6\right)}$$

36 ni -192 ga qo'shish.

$$x=\frac{-6±\sqrt{-156}}{2\left(-6\right)}$$

-156 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{39}i}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$x=\frac{-6±2\sqrt{39}i}{-12}$$

x=\frac{-6±2\sqrt{39}i}{-12} tenglamasini yeching, bunda ± musbat. -6 ni 2i\sqrt{39} ga qo'shish.

$$x=\frac{-6+2\sqrt{39}i}{-12}$$

-6+2i\sqrt{39} ni -12 ga bo'lish.

$$x=-\frac{\sqrt{39}i}{6}+\frac{1}{2}$$

x=\frac{-6±2\sqrt{39}i}{-12} tenglamasini yeching, bunda ± manfiy. -6 dan 2i\sqrt{39} ni ayirish.

$$x=\frac{-2\sqrt{39}i-6}{-12}$$

-6-2i\sqrt{39} ni -12 ga bo'lish.

$$x=\frac{\sqrt{39}i}{6}+\frac{1}{2}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{39}i}{6}+\frac{1}{2} x=\frac{\sqrt{39}i}{6}+\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x-1 ga -3x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-6x^{2}+11x-4=-6x+11x+4$$

5x ni olish uchun -6x va 11x ni birlashtirish.

$$-6x^{2}+11x-4=5x+4$$

Ikkala tarafdan 5x ni ayirish.

$$-6x^{2}+11x-4-5x=4$$

6x ni olish uchun 11x va -5x ni birlashtirish.

$$-6x^{2}+6x-4=4$$

4 ni ikki tarafga qo’shing.

$$-6x^{2}+6x=4+4$$

8 olish uchun 4 va 4'ni qo'shing.

$$-6x^{2}+6x=8$$

Ikki tarafini -6 ga bo‘ling.

$$\frac{-6x^{2}+6x}{-6}=\frac{8}{-6}$$

-6 ga bo'lish -6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{6}{-6}x=\frac{8}{-6}$$

6 ni -6 ga bo'lish.

$$x^{2}-x=\frac{8}{-6}$$

\frac{8}{-6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

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

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-\frac{4}{3}+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=-\frac{4}{3}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{4}{3} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-x+\frac{1}{4}=-\frac{13}{12}$$

x^{2}-x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{2}\right)^{2}=-\frac{13}{12}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{13}{12}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{\sqrt{39}i}{6} x-\frac{1}{2}=-\frac{\sqrt{39}i}{6}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{39}i}{6}+\frac{1}{2} x=-\frac{\sqrt{39}i}{6}+\frac{1}{2}$$