left(3x+2right)^(x+3)=x+4 eching

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

x uchun yechish

$$x=\frac{\sqrt{19}-5}{3}\approx -0,213700352$$

$$x=\frac{-\sqrt{19}-5}{3}\approx -3,119632981$$

Kvadrat tenglamalaridan foydalanish qoidalari

1 daraja ko‘rsatkichini 3x+2 ga hisoblang va 3x+2 ni qiymatni oling.

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

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

$$3x^{2}+11x+6=x+4$$

Ikkala tarafdan x ni ayirish.

$$3x^{2}+11x+6-x=4$$

10x ni olish uchun 11x va -x ni birlashtirish.

$$3x^{2}+10x+6=4$$

Ikkala tarafdan 4 ni ayirish.

$$3x^{2}+10x+6-4=0$$

2 olish uchun 6 dan 4 ni ayirish.

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

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

$$x=\frac{-10±\sqrt{10^{2}-4\times 3\times 2}}{2\times 3}$$

10 kvadratini chiqarish.

$$x=\frac{-10±\sqrt{100-4\times 3\times 2}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100-12\times 2}}{2\times 3}$$

-12 ni 2 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100-24}}{2\times 3}$$

100 ni -24 ga qo'shish.

$$x=\frac{-10±\sqrt{76}}{2\times 3}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-10±2\sqrt{19}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-10±2\sqrt{19}}{6}$$

x=\frac{-10±2\sqrt{19}}{6} tenglamasini yeching, bunda ± musbat. -10 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}-10}{6}$$

-10+2\sqrt{19} ni 6 ga bo'lish.

$$x=\frac{\sqrt{19}-5}{3}$$

x=\frac{-10±2\sqrt{19}}{6} tenglamasini yeching, bunda ± manfiy. -10 dan 2\sqrt{19} ni ayirish.

$$x=\frac{-2\sqrt{19}-10}{6}$$

-10-2\sqrt{19} ni 6 ga bo'lish.

$$x=\frac{-\sqrt{19}-5}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{19}-5}{3} x=\frac{-\sqrt{19}-5}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

1 daraja ko‘rsatkichini 3x+2 ga hisoblang va 3x+2 ni qiymatni oling.

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

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

$$3x^{2}+11x+6=x+4$$

Ikkala tarafdan x ni ayirish.

$$3x^{2}+11x+6-x=4$$

10x ni olish uchun 11x va -x ni birlashtirish.

$$3x^{2}+10x+6=4$$

Ikkala tarafdan 6 ni ayirish.

$$3x^{2}+10x=4-6$$

-2 olish uchun 4 dan 6 ni ayirish.

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

Ikki tarafini 3 ga bo‘ling.

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

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

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

\frac{10}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{3} olish uchun. Keyin, \frac{5}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{10}{3}x+\left(\frac{5}{3}\right)^{2}=-\frac{2}{3}+\left(\frac{5}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{3} kvadratini chiqarish.

$$x^{2}+\frac{10}{3}x+\frac{25}{9}=-\frac{2}{3}+\frac{25}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{2}{3} ni \frac{25}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{10}{3}x+\frac{25}{9}=\frac{19}{9}$$

x^{2}+\frac{10}{3}x+\frac{25}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{5}{3}\right)^{2}=\frac{19}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{3}\right)^{2}}=\sqrt{\frac{19}{9}}$$

Qisqartirish.

$$x+\frac{5}{3}=\frac{\sqrt{19}}{3} x+\frac{5}{3}=-\frac{\sqrt{19}}{3}$$

Tenglamaning ikkala tarafidan \frac{5}{3} ni ayirish.

$$x=\frac{\sqrt{19}-5}{3} x=\frac{-\sqrt{19}-5}{3}$$