4m^2+3m+6=0 eching

$$4 m ^ { 2 } + 3 m + 6 = 0$$

m uchun yechish

$$m=\frac{-3+\sqrt{87}i}{8}\approx -0,375+1,165922382i$$

$$m=\frac{-\sqrt{87}i-3}{8}\approx -0,375-1,165922382i$$

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.

$$4m^{2}+3m+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 3 ni b va 6 ni c bilan almashtiring.

$$m=\frac{-3±\sqrt{3^{2}-4\times 4\times 6}}{2\times 4}$$

3 kvadratini chiqarish.

$$m=\frac{-3±\sqrt{9-4\times 4\times 6}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$m=\frac{-3±\sqrt{9-16\times 6}}{2\times 4}$$

-16 ni 6 marotabaga ko'paytirish.

$$m=\frac{-3±\sqrt{9-96}}{2\times 4}$$

9 ni -96 ga qo'shish.

$$m=\frac{-3±\sqrt{-87}}{2\times 4}$$

-87 ning kvadrat ildizini chiqarish.

$$m=\frac{-3±\sqrt{87}i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$m=\frac{-3±\sqrt{87}i}{8}$$

m=\frac{-3±\sqrt{87}i}{8} tenglamasini yeching, bunda ± musbat. -3 ni i\sqrt{87} ga qo'shish.

$$m=\frac{-3+\sqrt{87}i}{8}$$

m=\frac{-3±\sqrt{87}i}{8} tenglamasini yeching, bunda ± manfiy. -3 dan i\sqrt{87} ni ayirish.

$$m=\frac{-\sqrt{87}i-3}{8}$$

Tenglama yechildi.

$$m=\frac{-3+\sqrt{87}i}{8} m=\frac{-\sqrt{87}i-3}{8}$$

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.

$$4m^{2}+3m+6=0$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$4m^{2}+3m+6-6=-6$$

O‘zidan 6 ayirilsa 0 qoladi.

$$4m^{2}+3m=-6$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4m^{2}+3m}{4}=-\frac{6}{4}$$

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

$$m^{2}+\frac{3}{4}m=-\frac{6}{4}$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$m^{2}+\frac{3}{4}m=-\frac{3}{2}$$

\frac{3}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{8} olish uchun. Keyin, \frac{3}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}+\frac{3}{4}m+\left(\frac{3}{8}\right)^{2}=-\frac{3}{2}+\left(\frac{3}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{8} kvadratini chiqarish.

$$m^{2}+\frac{3}{4}m+\frac{9}{64}=-\frac{3}{2}+\frac{9}{64}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{3}{2} ni \frac{9}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$m^{2}+\frac{3}{4}m+\frac{9}{64}=-\frac{87}{64}$$

m^{2}+\frac{3}{4}m+\frac{9}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m+\frac{3}{8}\right)^{2}=-\frac{87}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m+\frac{3}{8}\right)^{2}}=\sqrt{-\frac{87}{64}}$$

Qisqartirish.

$$m+\frac{3}{8}=\frac{\sqrt{87}i}{8} m+\frac{3}{8}=-\frac{\sqrt{87}i}{8}$$

Tenglamaning ikkala tarafidan \frac{3}{8} ni ayirish.

$$m=\frac{-3+\sqrt{87}i}{8} m=\frac{-\sqrt{87}i-3}{8}$$