3(x+2)(x-2)=(x-4)+8x eching

$$3(x+2)(x-2)=(x-4)+8x$$

x uchun yechish

$$x=\frac{\sqrt{177}}{6}+\frac{3}{2}\approx 3,717355783$$

$$x=-\frac{\sqrt{177}}{6}+\frac{3}{2}\approx -0,717355783$$

Kvadrat tenglamalaridan foydalanish qoidalari

3 ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(3x+6\right)\left(x-2\right)=x-4+8x$$

3x+6 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{2}-12=x-4+8x$$

9x ni olish uchun x va 8x ni birlashtirish.

$$3x^{2}-12=9x-4$$

Ikkala tarafdan 9x ni ayirish.

$$3x^{2}-12-9x=-4$$

4 ni ikki tarafga qo’shing.

$$3x^{2}-12-9x+4=0$$

-8 olish uchun -12 va 4'ni qo'shing.

$$3x^{2}-8-9x=0$$

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.

$$3x^{2}-9x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -9 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 3\left(-8\right)}}{2\times 3}$$

-9 kvadratini chiqarish.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 3\left(-8\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81-12\left(-8\right)}}{2\times 3}$$

-12 ni -8 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81+96}}{2\times 3}$$

81 ni 96 ga qo'shish.

$$x=\frac{-\left(-9\right)±\sqrt{177}}{2\times 3}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±\sqrt{177}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{9±\sqrt{177}}{6}$$

x=\frac{9±\sqrt{177}}{6} tenglamasini yeching, bunda ± musbat. 9 ni \sqrt{177} ga qo'shish.

$$x=\frac{\sqrt{177}+9}{6}$$

9+\sqrt{177} ni 6 ga bo'lish.

$$x=\frac{\sqrt{177}}{6}+\frac{3}{2}$$

x=\frac{9±\sqrt{177}}{6} tenglamasini yeching, bunda ± manfiy. 9 dan \sqrt{177} ni ayirish.

$$x=\frac{9-\sqrt{177}}{6}$$

9-\sqrt{177} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{177}}{6}+\frac{3}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{177}}{6}+\frac{3}{2} x=-\frac{\sqrt{177}}{6}+\frac{3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

3 ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(3x+6\right)\left(x-2\right)=x-4+8x$$

3x+6 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{2}-12=x-4+8x$$

9x ni olish uchun x va 8x ni birlashtirish.

$$3x^{2}-12=9x-4$$

Ikkala tarafdan 9x ni ayirish.

$$3x^{2}-12-9x=-4$$

12 ni ikki tarafga qo’shing.

$$3x^{2}-9x=-4+12$$

8 olish uchun -4 va 12'ni qo'shing.

$$3x^{2}-9x=8$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-9x}{3}=\frac{8}{3}$$

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

$$x^{2}+\left(-\frac{9}{3}\right)x=\frac{8}{3}$$

-9 ni 3 ga bo'lish.

$$x^{2}-3x=\frac{8}{3}$$

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

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=\frac{8}{3}+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=\frac{8}{3}+\frac{9}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{8}{3} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-3x+\frac{9}{4}=\frac{59}{12}$$

x^{2}-3x+\frac{9}{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.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{59}{12}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{59}{12}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{\sqrt{177}}{6} x-\frac{3}{2}=-\frac{\sqrt{177}}{6}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{177}}{6}+\frac{3}{2} x=-\frac{\sqrt{177}}{6}+\frac{3}{2}$$