(2x-3)(x-4)=18 eching

$$(2x-3)(x-4)=18$$

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

$$x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x-3 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-11x+12=18$$

Ikkala tarafdan 18 ni ayirish.

$$2x^{2}-11x+12-18=0$$

-6 olish uchun 12 dan 18 ni ayirish.

$$2x^{2}-11x-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -11 ni b va -6 ni c bilan almashtiring.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

-11 kvadratini chiqarish.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\times 2\left(-6\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121-8\left(-6\right)}}{2\times 2}$$

-8 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121+48}}{2\times 2}$$

121 ni 48 ga qo'shish.

$$x=\frac{-\left(-11\right)±\sqrt{169}}{2\times 2}$$

169 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-11\right)±13}{2\times 2}$$

-11 ning teskarisi 11 ga teng.

$$x=\frac{11±13}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{11±13}{4}$$

x=\frac{11±13}{4} tenglamasini yeching, bunda ± musbat. 11 ni 13 ga qo'shish.

$$x=\frac{24}{4}$$

24 ni 4 ga bo'lish.

$$x=6$$

x=\frac{11±13}{4} tenglamasini yeching, bunda ± manfiy. 11 dan 13 ni ayirish.

$$x=-\frac{2}{4}$$

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

2x-3 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-11x+12=18$$

Ikkala tarafdan 12 ni ayirish.

$$2x^{2}-11x=18-12$$

6 olish uchun 18 dan 12 ni ayirish.

$$2x^{2}-11x=6$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-11x}{2}=\frac{6}{2}$$

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

$$x^{2}-\frac{11}{2}x=\frac{6}{2}$$

6 ni 2 ga bo'lish.

$$x^{2}-\frac{11}{2}x=3$$

-\frac{11}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{11}{4} olish uchun. Keyin, -\frac{11}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{11}{2}x+\left(-\frac{11}{4}\right)^{2}=3+\left(-\frac{11}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{4} kvadratini chiqarish.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=3+\frac{121}{16}$$

3 ni \frac{121}{16} ga qo'shish.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=\frac{169}{16}$$

x^{2}-\frac{11}{2}x+\frac{121}{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.

$$\left(x-\frac{11}{4}\right)^{2}=\frac{169}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{11}{4}\right)^{2}}=\sqrt{\frac{169}{16}}$$

Qisqartirish.

$$x-\frac{11}{4}=\frac{13}{4} x-\frac{11}{4}=-\frac{13}{4}$$

\frac{11}{4} ni tenglamaning ikkala tarafiga qo'shish.

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