(x-11)(x-085)+015*01=0 eching

$$( x - 11 ) ( x - 085 ) + 015 \times 01 = 0$$

x uchun yechish

$$x=0$$

$$x=11$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 85 ni ko'paytirish.

$$\left(x-11\right)\left(x-0\right)+0\times 15\times 0\times 1=0$$

x-11 ga x-0 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 15\times 0\times 1=0$$

0 hosil qilish uchun 0 va 15 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 0\times 1=0$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 1=0$$

0 hosil qilish uchun 0 va 1 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x\left(x-0\right)-11\left(x-0\right)=0$$

Shartlarni qayta saralash.

$$xx-11x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

x omili.

$$x\left(x-11\right)=0$$

Tenglamani yechish uchun x=0 va x-11=0 ni yeching.

$$x=0 x=11$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 85 ni ko'paytirish.

$$\left(x-11\right)\left(x-0\right)+0\times 15\times 0\times 1=0$$

x-11 ga x-0 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 15\times 0\times 1=0$$

0 hosil qilish uchun 0 va 15 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 0\times 1=0$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 1=0$$

0 hosil qilish uchun 0 va 1 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x\left(x-0\right)-11\left(x-0\right)=0$$

Shartlarni qayta saralash.

$$xx-11x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -11 ni b va 0 ni c bilan almashtiring.

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

\left(-11\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-11\right)±11}{2}$$

-11 ning teskarisi 11 ga teng.

$$x=\frac{11±11}{2}$$

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

$$x=\frac{22}{2}$$

22 ni 2 ga bo'lish.

$$x=11$$

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

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=11 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 85 ni ko'paytirish.

$$\left(x-11\right)\left(x-0\right)+0\times 15\times 0\times 1=0$$

x-11 ga x-0 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 15\times 0\times 1=0$$

0 hosil qilish uchun 0 va 15 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 0\times 1=0$$

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 1=0$$

0 hosil qilish uchun 0 va 1 ni ko'paytirish.

$$x\left(x-0\right)-11\left(x-0\right)+0=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x\left(x-0\right)-11\left(x-0\right)=0$$

Shartlarni qayta saralash.

$$xx-11x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{2} kvadratini chiqarish.

$$x^{2}-11x+\frac{121}{4}=\frac{121}{4}$$

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

$$\left(x-\frac{11}{2}\right)^{2}=\frac{121}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

\frac{11}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=11 x=0$$