-x*(x-81)=0 eching

$$- x \cdot ( x - 81 ) = 0$$

x uchun yechish

$$x=81$$

$$x=0$$

Faktorlash qadamlari

-x ga x-81 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-x\right)x-81\left(-x\right)=0$$

81 hosil qilish uchun -81 va -1 ni ko'paytirish.

$$\left(-x\right)x+81x=0$$

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

$$-x^{2}+81x=0$$

x omili.

$$x\left(-x+81\right)=0$$

Tenglamani yechish uchun x=0 va -x+81=0 ni yeching.

$$x=0 x=81$$

Kvadrat tenglamalaridan foydalanish qoidalari

-x ga x-81 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-x\right)x-81\left(-x\right)=0$$

81 hosil qilish uchun -81 va -1 ni ko'paytirish.

$$\left(-x\right)x+81x=0$$

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

$$-x^{2}+81x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 81 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-81±\sqrt{81^{2}}}{2\left(-1\right)}$$

81^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-81±81}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-81±81}{-2}$$

x=\frac{-81±81}{-2} tenglamasini yeching, bunda ± musbat. -81 ni 81 ga qo'shish.

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

0 ni -2 ga bo'lish.

$$x=0$$

x=\frac{-81±81}{-2} tenglamasini yeching, bunda ± manfiy. -81 dan 81 ni ayirish.

$$x=-\frac{162}{-2}$$

-162 ni -2 ga bo'lish.

$$x=81$$

Tenglama yechildi.

$$x=0 x=81$$

Kvadratni yakunlash bo'yicha qadamlar

-x ga x-81 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-x\right)x-81\left(-x\right)=0$$

81 hosil qilish uchun -81 va -1 ni ko'paytirish.

$$\left(-x\right)x+81x=0$$

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

$$-x^{2}+81x=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+81x}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{81}{-1}x=\frac{0}{-1}$$

81 ni -1 ga bo'lish.

$$x^{2}-81x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$x^{2}-81x=0$$

-81 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{81}{2} olish uchun. Keyin, -\frac{81}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-81x+\left(-\frac{81}{2}\right)^{2}=\left(-\frac{81}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{81}{2} kvadratini chiqarish.

$$x^{2}-81x+\frac{6561}{4}=\frac{6561}{4}$$

x^{2}-81x+\frac{6561}{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.

$$\left(x-\frac{81}{2}\right)^{2}=\frac{6561}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{81}{2}\right)^{2}}=\sqrt{\frac{6561}{4}}$$

Qisqartirish.

$$x-\frac{81}{2}=\frac{81}{2} x-\frac{81}{2}=-\frac{81}{2}$$

\frac{81}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=81 x=0$$