(2x-3)*(x+1)=3 eching

$$(2x-3) \times (x+1)=3$$

x uchun yechish

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

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

Ikkala tarafdan 3 ni ayirish.

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

-6 olish uchun -3 dan 3 ni ayirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -1 ni b va -6 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 2\left(-6\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-8\left(-6\right)}}{2\times 2}$$

-8 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+48}}{2\times 2}$$

1 ni 48 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{49}}{2\times 2}$$

49 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±7}{2\times 2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±7}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{1±7}{4}$$

x=\frac{1±7}{4} tenglamasini yeching, bunda ± musbat. 1 ni 7 ga qo'shish.

$$x=\frac{8}{4}$$

8 ni 4 ga bo'lish.

$$x=2$$

x=\frac{1±7}{4} tenglamasini yeching, bunda ± manfiy. 1 dan 7 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.

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

Kvadratni yakunlash bo'yicha qadamlar

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

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

3 ni ikki tarafga qo’shing.

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

6 olish uchun 3 va 3'ni qo'shing.

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

Ikki tarafini 2 ga bo‘ling.

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

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

$$x^{2}-\frac{1}{2}x=\frac{6}{2}$$

6 ni 2 ga bo'lish.

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

-\frac{1}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{4} olish uchun. Keyin, -\frac{1}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4} kvadratini chiqarish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=3+\frac{1}{16}$$

3 ni \frac{1}{16} ga qo'shish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{49}{16}$$

x^{2}-\frac{1}{2}x+\frac{1}{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.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{49}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Qisqartirish.

$$x-\frac{1}{4}=\frac{7}{4} x-\frac{1}{4}=-\frac{7}{4}$$

\frac{1}{4} ni tenglamaning ikkala tarafiga qo'shish.

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