4x^2-8x+8=0 eching

$$4 x ^ { 2 } - 8 x + 8 = 0$$

x uchun yechish (complex solution)

$$x=1+i$$

$$x=1-i$$

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.

$$4x^{2}-8x+8=0$$

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

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

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 4\times 8}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-16\times 8}}{2\times 4}$$

-16 ni 8 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-128}}{2\times 4}$$

64 ni -128 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{-64}}{2\times 4}$$

-64 ning kvadrat ildizini chiqarish.

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

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±8i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{8±8i}{8}$$

x=\frac{8±8i}{8} tenglamasini yeching, bunda ± musbat. 8 ni 8i ga qo'shish.

$$x=\frac{8+8i}{8}$$

8+8i ni 8 ga bo'lish.

$$x=1+i$$

x=\frac{8±8i}{8} tenglamasini yeching, bunda ± manfiy. 8 dan 8i ni ayirish.

$$x=\frac{8-8i}{8}$$

8-8i ni 8 ga bo'lish.

$$x=1-i$$

Tenglama yechildi.

$$x=1+i x=1-i$$

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.

$$4x^{2}-8x+8=0$$

Tenglamaning ikkala tarafidan 8 ni ayirish.

$$4x^{2}-8x+8-8=-8$$

O‘zidan 8 ayirilsa 0 qoladi.

$$4x^{2}-8x=-8$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-8x}{4}=-\frac{8}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

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

-8 ni 4 ga bo'lish.

$$x^{2}-2x=-\frac{8}{4}$$

-8 ni 4 ga bo'lish.

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

-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.

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

-2 ni 1 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-1=i x-1=-i$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=1+i x=1-i$$