3n^2+6n-13=-5 eching

$$3 n ^ { 2 } + 6 n - 13 = - 5$$

n uchun yechish

$$n=\frac{\sqrt{33}}{3}-1\approx 0,914854216$$

$$n=-\frac{\sqrt{33}}{3}-1\approx -2,914854216$$

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.

$$3n^{2}+6n-13=-5$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$3n^{2}+6n-13-\left(-5\right)=-5-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$3n^{2}+6n-13-\left(-5\right)=0$$

-13 dan -5 ni ayirish.

$$3n^{2}+6n-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 6 ni b va -8 ni c bilan almashtiring.

$$n=\frac{-6±\sqrt{6^{2}-4\times 3\left(-8\right)}}{2\times 3}$$

6 kvadratini chiqarish.

$$n=\frac{-6±\sqrt{36-4\times 3\left(-8\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$n=\frac{-6±\sqrt{36-12\left(-8\right)}}{2\times 3}$$

-12 ni -8 marotabaga ko'paytirish.

$$n=\frac{-6±\sqrt{36+96}}{2\times 3}$$

36 ni 96 ga qo'shish.

$$n=\frac{-6±\sqrt{132}}{2\times 3}$$

132 ning kvadrat ildizini chiqarish.

$$n=\frac{-6±2\sqrt{33}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$n=\frac{-6±2\sqrt{33}}{6}$$

n=\frac{-6±2\sqrt{33}}{6} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{33} ga qo'shish.

$$n=\frac{2\sqrt{33}-6}{6}$$

-6+2\sqrt{33} ni 6 ga bo'lish.

$$n=\frac{\sqrt{33}}{3}-1$$

n=\frac{-6±2\sqrt{33}}{6} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{33} ni ayirish.

$$n=\frac{-2\sqrt{33}-6}{6}$$

-6-2\sqrt{33} ni 6 ga bo'lish.

$$n=-\frac{\sqrt{33}}{3}-1$$

Tenglama yechildi.

$$n=\frac{\sqrt{33}}{3}-1 n=-\frac{\sqrt{33}}{3}-1$$

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.

$$3n^{2}+6n-13=-5$$

13 ni tenglamaning ikkala tarafiga qo'shish.

$$3n^{2}+6n-13-\left(-13\right)=-5-\left(-13\right)$$

O‘zidan -13 ayirilsa 0 qoladi.

$$3n^{2}+6n=-5-\left(-13\right)$$

-5 dan -13 ni ayirish.

$$3n^{2}+6n=8$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3n^{2}+6n}{3}=\frac{8}{3}$$

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

$$n^{2}+\frac{6}{3}n=\frac{8}{3}$$

6 ni 3 ga bo'lish.

$$n^{2}+2n=\frac{8}{3}$$

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.

$$n^{2}+2n+1^{2}=\frac{8}{3}+1^{2}$$

1 kvadratini chiqarish.

$$n^{2}+2n+1=\frac{8}{3}+1$$

\frac{8}{3} ni 1 ga qo'shish.

$$n^{2}+2n+1=\frac{11}{3}$$

n^{2}+2n+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.

$$\left(n+1\right)^{2}=\frac{11}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n+1\right)^{2}}=\sqrt{\frac{11}{3}}$$

Qisqartirish.

$$n+1=\frac{\sqrt{33}}{3} n+1=-\frac{\sqrt{33}}{3}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$n=\frac{\sqrt{33}}{3}-1 n=-\frac{\sqrt{33}}{3}-1$$