3x^2+881x+10086=3 eching

$$3 x ^ { 2 } + 881 x + 10086 = 3$$

x uchun yechish

$$x=\frac{\sqrt{655165}-881}{6}\approx -11,929561044$$

$$x=\frac{-\sqrt{655165}-881}{6}\approx -281,737105622$$

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.

$$3x^{2}+881x+10086=3$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$3x^{2}+881x+10086-3=3-3$$

O‘zidan 3 ayirilsa 0 qoladi.

$$3x^{2}+881x+10086-3=0$$

10086 dan 3 ni ayirish.

$$3x^{2}+881x+10083=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 881 ni b va 10083 ni c bilan almashtiring.

$$x=\frac{-881±\sqrt{881^{2}-4\times 3\times 10083}}{2\times 3}$$

881 kvadratini chiqarish.

$$x=\frac{-881±\sqrt{776161-4\times 3\times 10083}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-881±\sqrt{776161-12\times 10083}}{2\times 3}$$

-12 ni 10083 marotabaga ko'paytirish.

$$x=\frac{-881±\sqrt{776161-120996}}{2\times 3}$$

776161 ni -120996 ga qo'shish.

$$x=\frac{-881±\sqrt{655165}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-881±\sqrt{655165}}{6}$$

x=\frac{-881±\sqrt{655165}}{6} tenglamasini yeching, bunda ± musbat. -881 ni \sqrt{655165} ga qo'shish.

$$x=\frac{\sqrt{655165}-881}{6}$$

x=\frac{-881±\sqrt{655165}}{6} tenglamasini yeching, bunda ± manfiy. -881 dan \sqrt{655165} ni ayirish.

$$x=\frac{-\sqrt{655165}-881}{6}$$

Tenglama yechildi.

$$x=\frac{\sqrt{655165}-881}{6} x=\frac{-\sqrt{655165}-881}{6}$$

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.

$$3x^{2}+881x+10086=3$$

Tenglamaning ikkala tarafidan 10086 ni ayirish.

$$3x^{2}+881x+10086-10086=3-10086$$

O‘zidan 10086 ayirilsa 0 qoladi.

$$3x^{2}+881x=3-10086$$

3 dan 10086 ni ayirish.

$$3x^{2}+881x=-10083$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}+881x}{3}=-\frac{10083}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{881}{3}x=-\frac{10083}{3}$$

-10083 ni 3 ga bo'lish.

$$x^{2}+\frac{881}{3}x=-3361$$

\frac{881}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{881}{6} olish uchun. Keyin, \frac{881}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{881}{3}x+\left(\frac{881}{6}\right)^{2}=-3361+\left(\frac{881}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{881}{6} kvadratini chiqarish.

$$x^{2}+\frac{881}{3}x+\frac{776161}{36}=-3361+\frac{776161}{36}$$

-3361 ni \frac{776161}{36} ga qo'shish.

$$x^{2}+\frac{881}{3}x+\frac{776161}{36}=\frac{655165}{36}$$

x^{2}+\frac{881}{3}x+\frac{776161}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{881}{6}\right)^{2}=\frac{655165}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{881}{6}\right)^{2}}=\sqrt{\frac{655165}{36}}$$

Qisqartirish.

$$x+\frac{881}{6}=\frac{\sqrt{655165}}{6} x+\frac{881}{6}=-\frac{\sqrt{655165}}{6}$$

Tenglamaning ikkala tarafidan \frac{881}{6} ni ayirish.

$$x=\frac{\sqrt{655165}-881}{6} x=\frac{-\sqrt{655165}-881}{6}$$