(2x+1)(x-2)=7 eching

$$( 2 x + 1 ) ( x - 2 ) = 7$$

x uchun yechish

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

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$2x^{2}-3x-2=7$$

Ikkala tarafdan 7 ni ayirish.

$$2x^{2}-3x-2-7=0$$

-9 olish uchun -2 dan 7 ni ayirish.

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

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

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

-3 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

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

-8 ni -9 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+72}}{2\times 2}$$

9 ni 72 ga qo'shish.

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

81 ning kvadrat ildizini chiqarish.

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

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±9}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{3±9}{4}$$

x=\frac{3±9}{4} tenglamasini yeching, bunda ± musbat. 3 ni 9 ga qo'shish.

$$x=\frac{12}{4}$$

12 ni 4 ga bo'lish.

$$x=3$$

x=\frac{3±9}{4} tenglamasini yeching, bunda ± manfiy. 3 dan 9 ni ayirish.

$$x=-\frac{6}{4}$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

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

$$2x^{2}-3x-2=7$$

2 ni ikki tarafga qo’shing.

$$2x^{2}-3x=7+2$$

9 olish uchun 7 va 2'ni qo'shing.

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

Ikki tarafini 2 ga bo‘ling.

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

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

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

-\frac{3}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{4} olish uchun. Keyin, -\frac{3}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{3}{2}x+\left(-\frac{3}{4}\right)^{2}=\frac{9}{2}+\left(-\frac{3}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{4} kvadratini chiqarish.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{9}{2}+\frac{9}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{9}{2} ni \frac{9}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{81}{16}$$

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

$$\left(x-\frac{3}{4}\right)^{2}=\frac{81}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{\frac{81}{16}}$$

Qisqartirish.

$$x-\frac{3}{4}=\frac{9}{4} x-\frac{3}{4}=-\frac{9}{4}$$

\frac{3}{4} ni tenglamaning ikkala tarafiga qo'shish.

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