(x-7)(x-9)=195 eching

$$( x - 7 ) ( x - 9 ) = 195$$

x uchun yechish

$$x=-6$$

$$x=22$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-7 ga x-9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-16x+63=195$$

Ikkala tarafdan 195 ni ayirish.

$$x^{2}-16x+63-195=0$$

-132 olish uchun 63 dan 195 ni ayirish.

$$x^{2}-16x-132=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -16 ni b va -132 ni c bilan almashtiring.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-132\right)}}{2}$$

-16 kvadratini chiqarish.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-132\right)}}{2}$$

-4 ni -132 marotabaga ko'paytirish.

$$x=\frac{-\left(-16\right)±\sqrt{256+528}}{2}$$

256 ni 528 ga qo'shish.

$$x=\frac{-\left(-16\right)±\sqrt{784}}{2}$$

784 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-16\right)±28}{2}$$

-16 ning teskarisi 16 ga teng.

$$x=\frac{16±28}{2}$$

x=\frac{16±28}{2} tenglamasini yeching, bunda ± musbat. 16 ni 28 ga qo'shish.

$$x=\frac{44}{2}$$

44 ni 2 ga bo'lish.

$$x=22$$

x=\frac{16±28}{2} tenglamasini yeching, bunda ± manfiy. 16 dan 28 ni ayirish.

$$x=-\frac{12}{2}$$

-12 ni 2 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=22 x=-6$$

Kvadratni yakunlash bo'yicha qadamlar

x-7 ga x-9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-16x+63=195$$

Ikkala tarafdan 63 ni ayirish.

$$x^{2}-16x=195-63$$

132 olish uchun 195 dan 63 ni ayirish.

$$x^{2}-16x=132$$

-16 ni bo‘lish, x shartining koeffitsienti, 2 ga -8 olish uchun. Keyin, -8 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-16x+\left(-8\right)^{2}=132+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

$$x^{2}-16x+64=132+64$$

132 ni 64 ga qo'shish.

$$x^{2}-16x+64=196$$

x^{2}-16x+64 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-8\right)^{2}=196$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{196}$$

Qisqartirish.

$$x-8=14 x-8=-14$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$x=22 x=-6$$