x^2-2x=-8 eching

$$x ^ { 2 } - 2 x = - 8$$

x uchun yechish (complex solution)

$$x=1+\sqrt{7}i\approx 1+2,645751311i$$

$$x=-\sqrt{7}i+1\approx 1-2,645751311i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}-2x=-8$$

8 ni tenglamaning ikkala tarafiga qo'shish.

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

O‘zidan -8 ayirilsa 0 qoladi.

$$x^{2}-2x-\left(-8\right)=0$$

0 dan -8 ni ayirish.

$$x^{2}-2x+8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va 8 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 8}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 8}}{2}$$

-4 ni 8 marotabaga ko'paytirish.

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

4 ni -32 ga qo'shish.

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

-28 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{7}i}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{7}i}{2}$$

x=\frac{2±2\sqrt{7}i}{2} tenglamasini yeching, bunda ± musbat. 2 ni 2i\sqrt{7} ga qo'shish.

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

2+2i\sqrt{7} ni 2 ga bo'lish.

$$x=1+\sqrt{7}i$$

x=\frac{2±2\sqrt{7}i}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 2i\sqrt{7} ni ayirish.

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

2-2i\sqrt{7} ni 2 ga bo'lish.

$$x=-\sqrt{7}i+1$$

Tenglama yechildi.

$$x=1+\sqrt{7}i x=-\sqrt{7}i+1$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}-2x=-8$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2x+1=-8+1$$

-8 ni 1 ga qo'shish.

$$x^{2}-2x+1=-7$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=-7$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{-7}$$

Qisqartirish.

$$x-1=\sqrt{7}i x-1=-\sqrt{7}i$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=1+\sqrt{7}i x=-\sqrt{7}i+1$$