3n^2+48n-2=0 eching

$$3 n ^ { 2 } + 48 n - 2 = 0$$

n uchun yechish

$$n=\frac{\sqrt{582}}{3}-8\approx 0,041558721$$

$$n=-\frac{\sqrt{582}}{3}-8\approx -16,041558721$$

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.

$$3n^{2}+48n-2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 48 ni b va -2 ni c bilan almashtiring.

$$n=\frac{-48±\sqrt{48^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

48 kvadratini chiqarish.

$$n=\frac{-48±\sqrt{2304-4\times 3\left(-2\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$n=\frac{-48±\sqrt{2304-12\left(-2\right)}}{2\times 3}$$

-12 ni -2 marotabaga ko'paytirish.

$$n=\frac{-48±\sqrt{2304+24}}{2\times 3}$$

2304 ni 24 ga qo'shish.

$$n=\frac{-48±\sqrt{2328}}{2\times 3}$$

2328 ning kvadrat ildizini chiqarish.

$$n=\frac{-48±2\sqrt{582}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$n=\frac{-48±2\sqrt{582}}{6}$$

n=\frac{-48±2\sqrt{582}}{6} tenglamasini yeching, bunda ± musbat. -48 ni 2\sqrt{582} ga qo'shish.

$$n=\frac{2\sqrt{582}-48}{6}$$

-48+2\sqrt{582} ni 6 ga bo'lish.

$$n=\frac{\sqrt{582}}{3}-8$$

n=\frac{-48±2\sqrt{582}}{6} tenglamasini yeching, bunda ± manfiy. -48 dan 2\sqrt{582} ni ayirish.

$$n=\frac{-2\sqrt{582}-48}{6}$$

-48-2\sqrt{582} ni 6 ga bo'lish.

$$n=-\frac{\sqrt{582}}{3}-8$$

Tenglama yechildi.

$$n=\frac{\sqrt{582}}{3}-8 n=-\frac{\sqrt{582}}{3}-8$$

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.

$$3n^{2}+48n-2=0$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$3n^{2}+48n-2-\left(-2\right)=-\left(-2\right)$$

O‘zidan -2 ayirilsa 0 qoladi.

$$3n^{2}+48n=-\left(-2\right)$$

0 dan -2 ni ayirish.

$$3n^{2}+48n=2$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3n^{2}+48n}{3}=\frac{2}{3}$$

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

$$n^{2}+\frac{48}{3}n=\frac{2}{3}$$

48 ni 3 ga bo'lish.

$$n^{2}+16n=\frac{2}{3}$$

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

$$n^{2}+16n+8^{2}=\frac{2}{3}+8^{2}$$

8 kvadratini chiqarish.

$$n^{2}+16n+64=\frac{2}{3}+64$$

\frac{2}{3} ni 64 ga qo'shish.

$$n^{2}+16n+64=\frac{194}{3}$$

n^{2}+16n+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.

$$\left(n+8\right)^{2}=\frac{194}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n+8\right)^{2}}=\sqrt{\frac{194}{3}}$$

Qisqartirish.

$$n+8=\frac{\sqrt{582}}{3} n+8=-\frac{\sqrt{582}}{3}$$

Tenglamaning ikkala tarafidan 8 ni ayirish.

$$n=\frac{\sqrt{582}}{3}-8 n=-\frac{\sqrt{582}}{3}-8$$