x(x-6sqrt{2})+65=0 eching

$$x(x-6 \sqrt{ 2 } )+65=0$$

x uchun yechish (complex solution)

$$x=3\sqrt{2}+\sqrt{47}i\approx 4,242640687+6,8556546i$$

$$x=-\sqrt{47}i+3\sqrt{2}\approx 4,242640687-6,8556546i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga x-6\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-6x\sqrt{2}+65=0$$

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.

$$x^{2}+\left(-6\sqrt{2}\right)x+65=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6\sqrt{2} ni b va 65 ni c bilan almashtiring.

$$x=\frac{-\left(-6\sqrt{2}\right)±\sqrt{\left(-6\sqrt{2}\right)^{2}-4\times 65}}{2}$$

-6\sqrt{2} kvadratini chiqarish.

$$x=\frac{-\left(-6\sqrt{2}\right)±\sqrt{72-4\times 65}}{2}$$

-4 ni 65 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\sqrt{2}\right)±\sqrt{72-260}}{2}$$

72 ni -260 ga qo'shish.

$$x=\frac{-\left(-6\sqrt{2}\right)±\sqrt{-188}}{2}$$

-188 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\sqrt{2}\right)±2\sqrt{47}i}{2}$$

-6\sqrt{2} ning teskarisi 6\sqrt{2} ga teng.

$$x=\frac{6\sqrt{2}±2\sqrt{47}i}{2}$$

x=\frac{6\sqrt{2}±2\sqrt{47}i}{2} tenglamasini yeching, bunda ± musbat. 6\sqrt{2} ni 2i\sqrt{47} ga qo'shish.

$$x=\frac{6\sqrt{2}+2\sqrt{47}i}{2}$$

6\sqrt{2}+2i\sqrt{47} ni 2 ga bo'lish.

$$x=3\sqrt{2}+\sqrt{47}i$$

x=\frac{6\sqrt{2}±2\sqrt{47}i}{2} tenglamasini yeching, bunda ± manfiy. 6\sqrt{2} dan 2i\sqrt{47} ni ayirish.

$$x=\frac{-2\sqrt{47}i+6\sqrt{2}}{2}$$

6\sqrt{2}-2i\sqrt{47} ni 2 ga bo'lish.

$$x=-\sqrt{47}i+3\sqrt{2}$$

Tenglama yechildi.

$$x=3\sqrt{2}+\sqrt{47}i x=-\sqrt{47}i+3\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x ga x-6\sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-6x\sqrt{2}+65=0$$

Ikkala tarafdan 65 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-6x\sqrt{2}=-65$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}+\left(-6\sqrt{2}\right)x=-65$$

-6\sqrt{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -3\sqrt{2} olish uchun. Keyin, -3\sqrt{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\left(-6\sqrt{2}\right)x+\left(-3\sqrt{2}\right)^{2}=-65+\left(-3\sqrt{2}\right)^{2}$$

-3\sqrt{2} kvadratini chiqarish.

$$x^{2}+\left(-6\sqrt{2}\right)x+18=-65+18$$

-65 ni 18 ga qo'shish.

$$x^{2}+\left(-6\sqrt{2}\right)x+18=-47$$

x^{2}+\left(-6\sqrt{2}\right)x+18 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\sqrt{2}\right)^{2}=-47$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\sqrt{2}\right)^{2}}=\sqrt{-47}$$

Qisqartirish.

$$x-3\sqrt{2}=\sqrt{47}i x-3\sqrt{2}=-\sqrt{47}i$$

3\sqrt{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=3\sqrt{2}+\sqrt{47}i x=-\sqrt{47}i+3\sqrt{2}$$