(x-1)(x-2)=30 eching

$$(x-1)(x-2)=30$$

x uchun yechish

$$x=-4$$

$$x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}-3x+2=30$$

Ikkala tarafdan 30 ni ayirish.

$$x^{2}-3x+2-30=0$$

-28 olish uchun 2 dan 30 ni ayirish.

$$x^{2}-3x-28=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va -28 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-28\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-28\right)}}{2}$$

-4 ni -28 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+112}}{2}$$

9 ni 112 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{121}}{2}$$

121 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±11}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±11}{2}$$

x=\frac{3±11}{2} tenglamasini yeching, bunda ± musbat. 3 ni 11 ga qo'shish.

$$x=\frac{14}{2}$$

14 ni 2 ga bo'lish.

$$x=7$$

x=\frac{3±11}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 11 ni ayirish.

$$x=-\frac{8}{2}$$

-8 ni 2 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=7 x=-4$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}-3x+2=30$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}-3x=30-2$$

28 olish uchun 30 dan 2 ni ayirish.

$$x^{2}-3x=28$$

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

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=28+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=28+\frac{9}{4}$$

28 ni \frac{9}{4} ga qo'shish.

$$x^{2}-3x+\frac{9}{4}=\frac{121}{4}$$

x^{2}-3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{121}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Qisqartirish.

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

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=-4$$