left(x-3right)left(2x+1right)=4 eching

$$\left( x-3 \right) \left( 2x+1 \right) =4$$

x uchun yechish

$$x=-1$$

$$x = \frac{7}{2} = 3\frac{1}{2} = 3,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$2x^{2}-5x-3=4$$

Ikkala tarafdan 4 ni ayirish.

$$2x^{2}-5x-3-4=0$$

-7 olish uchun -3 dan 4 ni ayirish.

$$2x^{2}-5x-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -5 ni b va -7 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-7\right)}}{2\times 2}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 2\left(-7\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-8\left(-7\right)}}{2\times 2}$$

-8 ni -7 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25+56}}{2\times 2}$$

25 ni 56 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{81}}{2\times 2}$$

81 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±9}{2\times 2}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±9}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{5±9}{4}$$

x=\frac{5±9}{4} tenglamasini yeching, bunda ± musbat. 5 ni 9 ga qo'shish.

$$x=\frac{14}{4}$$

\frac{14}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{7}{2}$$

x=\frac{5±9}{4} tenglamasini yeching, bunda ± manfiy. 5 dan 9 ni ayirish.

$$x=-\frac{4}{4}$$

-4 ni 4 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=\frac{7}{2} x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$2x^{2}-5x-3=4$$

3 ni ikki tarafga qo’shing.

$$2x^{2}-5x=4+3$$

7 olish uchun 4 va 3'ni qo'shing.

$$2x^{2}-5x=7$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-5x}{2}=\frac{7}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{5}{2}x=\frac{7}{2}$$

-\frac{5}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{4} olish uchun. Keyin, -\frac{5}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{5}{2}x+\left(-\frac{5}{4}\right)^{2}=\frac{7}{2}+\left(-\frac{5}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{4} kvadratini chiqarish.

$$x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{7}{2}+\frac{25}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{7}{2} ni \frac{25}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{81}{16}$$

x^{2}-\frac{5}{2}x+\frac{25}{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.

$$\left(x-\frac{5}{4}\right)^{2}=\frac{81}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{4}\right)^{2}}=\sqrt{\frac{81}{16}}$$

Qisqartirish.

$$x-\frac{5}{4}=\frac{9}{4} x-\frac{5}{4}=-\frac{9}{4}$$

\frac{5}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{7}{2} x=-1$$