-6x^2+12x-486=0 eching

$$- 6 x ^ { 2 } + 12 x - 486 = 0$$

x uchun yechish (complex solution)

$$x=1+4\sqrt{5}i\approx 1+8,94427191i$$

$$x=-4\sqrt{5}i+1\approx 1-8,94427191i$$

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.

$$-6x^{2}+12x-486=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -6 ni a, 12 ni b va -486 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-6\right)\left(-486\right)}}{2\left(-6\right)}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\left(-6\right)\left(-486\right)}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+24\left(-486\right)}}{2\left(-6\right)}$$

24 ni -486 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-11664}}{2\left(-6\right)}$$

144 ni -11664 ga qo'shish.

$$x=\frac{-12±\sqrt{-11520}}{2\left(-6\right)}$$

-11520 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±48\sqrt{5}i}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$x=\frac{-12±48\sqrt{5}i}{-12}$$

x=\frac{-12±48\sqrt{5}i}{-12} tenglamasini yeching, bunda ± musbat. -12 ni 48i\sqrt{5} ga qo'shish.

$$x=\frac{-12+48\sqrt{5}i}{-12}$$

-12+48i\sqrt{5} ni -12 ga bo'lish.

$$x=-4\sqrt{5}i+1$$

x=\frac{-12±48\sqrt{5}i}{-12} tenglamasini yeching, bunda ± manfiy. -12 dan 48i\sqrt{5} ni ayirish.

$$x=\frac{-48\sqrt{5}i-12}{-12}$$

-12-48i\sqrt{5} ni -12 ga bo'lish.

$$x=1+4\sqrt{5}i$$

Tenglama yechildi.

$$x=-4\sqrt{5}i+1 x=1+4\sqrt{5}i$$

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.

$$-6x^{2}+12x-486=0$$

486 ni tenglamaning ikkala tarafiga qo'shish.

$$-6x^{2}+12x-486-\left(-486\right)=-\left(-486\right)$$

O‘zidan -486 ayirilsa 0 qoladi.

$$-6x^{2}+12x=-\left(-486\right)$$

0 dan -486 ni ayirish.

$$-6x^{2}+12x=486$$

Ikki tarafini -6 ga bo‘ling.

$$\frac{-6x^{2}+12x}{-6}=\frac{486}{-6}$$

-6 ga bo'lish -6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{12}{-6}x=\frac{486}{-6}$$

12 ni -6 ga bo'lish.

$$x^{2}-2x=\frac{486}{-6}$$

486 ni -6 ga bo'lish.

$$x^{2}-2x=-81$$

-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.

$$x^{2}-2x+1=-81+1$$

-81 ni 1 ga qo'shish.

$$x^{2}-2x+1=-80$$

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.

$$\left(x-1\right)^{2}=-80$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{-80}$$

Qisqartirish.

$$x-1=4\sqrt{5}i x-1=-4\sqrt{5}i$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=1+4\sqrt{5}i x=-4\sqrt{5}i+1$$