1-2(x-3)(x-11)=0 eching

$$1 - 2 ( x - 3 ) ( x - 11 ) = 0$$

x uchun yechish

$$x=\frac{\sqrt{66}}{2}+7\approx 11,062019202$$

$$x=-\frac{\sqrt{66}}{2}+7\approx 2,937980798$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$1-2\left(x-3\right)\left(x-11\right)=0$$

-2 ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1+\left(-2x+6\right)\left(x-11\right)=0$$

-2x+6 ga x-11 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1-2x^{2}+28x-66=0$$

-65 olish uchun 1 dan 66 ni ayirish.

$$-65-2x^{2}+28x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-2x^{2}+28x-65=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 28 ni b va -65 ni c bilan almashtiring.

$$x=\frac{-28±\sqrt{28^{2}-4\left(-2\right)\left(-65\right)}}{2\left(-2\right)}$$

28 kvadratini chiqarish.

$$x=\frac{-28±\sqrt{784-4\left(-2\right)\left(-65\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-28±\sqrt{784+8\left(-65\right)}}{2\left(-2\right)}$$

8 ni -65 marotabaga ko'paytirish.

$$x=\frac{-28±\sqrt{784-520}}{2\left(-2\right)}$$

784 ni -520 ga qo'shish.

$$x=\frac{-28±\sqrt{264}}{2\left(-2\right)}$$

264 ning kvadrat ildizini chiqarish.

$$x=\frac{-28±2\sqrt{66}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-28±2\sqrt{66}}{-4}$$

x=\frac{-28±2\sqrt{66}}{-4} tenglamasini yeching, bunda ± musbat. -28 ni 2\sqrt{66} ga qo'shish.

$$x=\frac{2\sqrt{66}-28}{-4}$$

-28+2\sqrt{66} ni -4 ga bo'lish.

$$x=-\frac{\sqrt{66}}{2}+7$$

x=\frac{-28±2\sqrt{66}}{-4} tenglamasini yeching, bunda ± manfiy. -28 dan 2\sqrt{66} ni ayirish.

$$x=\frac{-2\sqrt{66}-28}{-4}$$

-28-2\sqrt{66} ni -4 ga bo'lish.

$$x=\frac{\sqrt{66}}{2}+7$$

Tenglama yechildi.

$$x=-\frac{\sqrt{66}}{2}+7 x=\frac{\sqrt{66}}{2}+7$$

Kvadratni yakunlash bo'yicha qadamlar

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$1-2\left(x-3\right)\left(x-11\right)=0$$

-2 ga x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1+\left(-2x+6\right)\left(x-11\right)=0$$

-2x+6 ga x-11 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1-2x^{2}+28x-66=0$$

-65 olish uchun 1 dan 66 ni ayirish.

$$-65-2x^{2}+28x=0$$

65 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-2x^{2}+28x=65$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+28x}{-2}=\frac{65}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{28}{-2}x=\frac{65}{-2}$$

28 ni -2 ga bo'lish.

$$x^{2}-14x=\frac{65}{-2}$$

65 ni -2 ga bo'lish.

$$x^{2}-14x=-\frac{65}{2}$$

-14 ni bo‘lish, x shartining koeffitsienti, 2 ga -7 olish uchun. Keyin, -7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-14x+\left(-7\right)^{2}=-\frac{65}{2}+\left(-7\right)^{2}$$

-7 kvadratini chiqarish.

$$x^{2}-14x+49=-\frac{65}{2}+49$$

-\frac{65}{2} ni 49 ga qo'shish.

$$x^{2}-14x+49=\frac{33}{2}$$

x^{2}-14x+49 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-7\right)^{2}=\frac{33}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-7\right)^{2}}=\sqrt{\frac{33}{2}}$$

Qisqartirish.

$$x-7=\frac{\sqrt{66}}{2} x-7=-\frac{\sqrt{66}}{2}$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{66}}{2}+7 x=-\frac{\sqrt{66}}{2}+7$$