(x-7)(x-5)=3 eching

$$( x - 7 ) ( x - 5 ) = 3$$

x uchun yechish

$$x=4$$

$$x=8$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-7 ga x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-12x+35=3$$

Ikkala tarafdan 3 ni ayirish.

$$x^{2}-12x+35-3=0$$

32 olish uchun 35 dan 3 ni ayirish.

$$x^{2}-12x+32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -12 ni b va 32 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 32}}{2}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 32}}{2}$$

-4 ni 32 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144-128}}{2}$$

144 ni -128 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{16}}{2}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±4}{2}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±4}{2}$$

x=\frac{12±4}{2} tenglamasini yeching, bunda ± musbat. 12 ni 4 ga qo'shish.

$$x=\frac{16}{2}$$

16 ni 2 ga bo'lish.

$$x=8$$

x=\frac{12±4}{2} tenglamasini yeching, bunda ± manfiy. 12 dan 4 ni ayirish.

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

8 ni 2 ga bo'lish.

$$x=4$$

Tenglama yechildi.

$$x=8 x=4$$

Kvadratni yakunlash bo'yicha qadamlar

x-7 ga x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-12x+35=3$$

Ikkala tarafdan 35 ni ayirish.

$$x^{2}-12x=3-35$$

-32 olish uchun 3 dan 35 ni ayirish.

$$x^{2}-12x=-32$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=-32+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=-32+36$$

-32 ni 36 ga qo'shish.

$$x^{2}-12x+36=4$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-6=2 x-6=-2$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=8 x=4$$