6x^2+12x-1134=0 eching

$$6 { x }^{ 2 } +12x-1134=0$$

x uchun yechish (complex solution)

$$x=\sqrt{190}-1\approx 12,784048752$$

$$x=-\left(\sqrt{190}+1\right)\approx -14,784048752$$

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.

$$6x^{2}+12x-1134=0$$

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 -1134 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\times 6\left(-1134\right)}}{2\times 6}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 6\left(-1134\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-24\left(-1134\right)}}{2\times 6}$$

-24 ni -1134 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+27216}}{2\times 6}$$

144 ni 27216 ga qo'shish.

$$x=\frac{-12±\sqrt{27360}}{2\times 6}$$

27360 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±12\sqrt{190}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{-12±12\sqrt{190}}{12}$$

x=\frac{-12±12\sqrt{190}}{12} tenglamasini yeching, bunda ± musbat. -12 ni 12\sqrt{190} ga qo'shish.

$$x=\frac{12\sqrt{190}-12}{12}$$

-12+12\sqrt{190} ni 12 ga bo'lish.

$$x=\sqrt{190}-1$$

x=\frac{-12±12\sqrt{190}}{12} tenglamasini yeching, bunda ± manfiy. -12 dan 12\sqrt{190} ni ayirish.

$$x=\frac{-12\sqrt{190}-12}{12}$$

-12-12\sqrt{190} ni 12 ga bo'lish.

$$x=-\sqrt{190}-1$$

Tenglama yechildi.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$

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.

$$6x^{2}+12x-1134=0$$

1134 ni tenglamaning ikkala tarafiga qo'shish.

$$6x^{2}+12x-1134-\left(-1134\right)=-\left(-1134\right)$$

O‘zidan -1134 ayirilsa 0 qoladi.

$$6x^{2}+12x=-\left(-1134\right)$$

0 dan -1134 ni ayirish.

$$6x^{2}+12x=1134$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}+12x}{6}=\frac{1134}{6}$$

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

$$x^{2}+\frac{12}{6}x=\frac{1134}{6}$$

12 ni 6 ga bo'lish.

$$x^{2}+2x=\frac{1134}{6}$$

1134 ni 6 ga bo'lish.

$$x^{2}+2x=189$$

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.

$$x^{2}+2x+1^{2}=189+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=189+1$$

189 ni 1 ga qo'shish.

$$x^{2}+2x+1=190$$

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.

$$\left(x+1\right)^{2}=190$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{190}$$

Qisqartirish.

$$x+1=\sqrt{190} x+1=-\sqrt{190}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$

x uchun yechish

$$x=\sqrt{190}-1\approx 12,784048752$$

$$x=-\sqrt{190}-1\approx -14,784048752$$

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.

$$6x^{2}+12x-1134=0$$

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 -1134 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\times 6\left(-1134\right)}}{2\times 6}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 6\left(-1134\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-24\left(-1134\right)}}{2\times 6}$$

-24 ni -1134 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+27216}}{2\times 6}$$

144 ni 27216 ga qo'shish.

$$x=\frac{-12±\sqrt{27360}}{2\times 6}$$

27360 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±12\sqrt{190}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{-12±12\sqrt{190}}{12}$$

x=\frac{-12±12\sqrt{190}}{12} tenglamasini yeching, bunda ± musbat. -12 ni 12\sqrt{190} ga qo'shish.

$$x=\frac{12\sqrt{190}-12}{12}$$

-12+12\sqrt{190} ni 12 ga bo'lish.

$$x=\sqrt{190}-1$$

x=\frac{-12±12\sqrt{190}}{12} tenglamasini yeching, bunda ± manfiy. -12 dan 12\sqrt{190} ni ayirish.

$$x=\frac{-12\sqrt{190}-12}{12}$$

-12-12\sqrt{190} ni 12 ga bo'lish.

$$x=-\sqrt{190}-1$$

Tenglama yechildi.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$

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.

$$6x^{2}+12x-1134=0$$

1134 ni tenglamaning ikkala tarafiga qo'shish.

$$6x^{2}+12x-1134-\left(-1134\right)=-\left(-1134\right)$$

O‘zidan -1134 ayirilsa 0 qoladi.

$$6x^{2}+12x=-\left(-1134\right)$$

0 dan -1134 ni ayirish.

$$6x^{2}+12x=1134$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}+12x}{6}=\frac{1134}{6}$$

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

$$x^{2}+\frac{12}{6}x=\frac{1134}{6}$$

12 ni 6 ga bo'lish.

$$x^{2}+2x=\frac{1134}{6}$$

1134 ni 6 ga bo'lish.

$$x^{2}+2x=189$$

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.

$$x^{2}+2x+1^{2}=189+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=189+1$$

189 ni 1 ga qo'shish.

$$x^{2}+2x+1=190$$

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.

$$\left(x+1\right)^{2}=190$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{190}$$

Qisqartirish.

$$x+1=\sqrt{190} x+1=-\sqrt{190}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\sqrt{190}-1 x=-\sqrt{190}-1$$