6x^2-13x+39=0 eching

$$6 x ^ { 2 } - 13 x + 39 = 0$$

x uchun yechish (complex solution)

$$x=\frac{13+\sqrt{767}i}{12}\approx 1,083333333+2,307897071i$$

$$x=\frac{-\sqrt{767}i+13}{12}\approx 1,083333333-2,307897071i$$

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.

$$6x^{2}-13x+39=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -13 ni b va 39 ni c bilan almashtiring.

$$x=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 6\times 39}}{2\times 6}$$

-13 kvadratini chiqarish.

$$x=\frac{-\left(-13\right)±\sqrt{169-4\times 6\times 39}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-13\right)±\sqrt{169-24\times 39}}{2\times 6}$$

-24 ni 39 marotabaga ko'paytirish.

$$x=\frac{-\left(-13\right)±\sqrt{169-936}}{2\times 6}$$

169 ni -936 ga qo'shish.

$$x=\frac{-\left(-13\right)±\sqrt{-767}}{2\times 6}$$

-767 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-13\right)±\sqrt{767}i}{2\times 6}$$

-13 ning teskarisi 13 ga teng.

$$x=\frac{13±\sqrt{767}i}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{13±\sqrt{767}i}{12}$$

x=\frac{13±\sqrt{767}i}{12} tenglamasini yeching, bunda ± musbat. 13 ni i\sqrt{767} ga qo'shish.

$$x=\frac{13+\sqrt{767}i}{12}$$

x=\frac{13±\sqrt{767}i}{12} tenglamasini yeching, bunda ± manfiy. 13 dan i\sqrt{767} ni ayirish.

$$x=\frac{-\sqrt{767}i+13}{12}$$

Tenglama yechildi.

$$x=\frac{13+\sqrt{767}i}{12} x=\frac{-\sqrt{767}i+13}{12}$$

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.

$$6x^{2}-13x+39=0$$

Tenglamaning ikkala tarafidan 39 ni ayirish.

$$6x^{2}-13x+39-39=-39$$

O‘zidan 39 ayirilsa 0 qoladi.

$$6x^{2}-13x=-39$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-13x}{6}=-\frac{39}{6}$$

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

$$x^{2}-\frac{13}{6}x=-\frac{39}{6}$$

\frac{-39}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{13}{6}x=-\frac{13}{2}$$

-\frac{13}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{13}{12} olish uchun. Keyin, -\frac{13}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{13}{6}x+\left(-\frac{13}{12}\right)^{2}=-\frac{13}{2}+\left(-\frac{13}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{13}{12} kvadratini chiqarish.

$$x^{2}-\frac{13}{6}x+\frac{169}{144}=-\frac{13}{2}+\frac{169}{144}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{13}{2} ni \frac{169}{144} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{13}{6}x+\frac{169}{144}=-\frac{767}{144}$$

x^{2}-\frac{13}{6}x+\frac{169}{144} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{13}{12}\right)^{2}=-\frac{767}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{13}{12}\right)^{2}}=\sqrt{-\frac{767}{144}}$$

Qisqartirish.

$$x-\frac{13}{12}=\frac{\sqrt{767}i}{12} x-\frac{13}{12}=-\frac{\sqrt{767}i}{12}$$

\frac{13}{12} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{13+\sqrt{767}i}{12} x=\frac{-\sqrt{767}i+13}{12}$$