2b^2+6b-1=2 eching

$$2 b ^ { 2 } + 6 b - 1 = 2$$

b uchun yechish

$$b=\frac{\sqrt{15}-3}{2}\approx 0,436491673$$

$$b=\frac{-\sqrt{15}-3}{2}\approx -3,436491673$$

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.

$$2b^{2}+6b-1=2$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$2b^{2}+6b-1-2=2-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$2b^{2}+6b-1-2=0$$

-1 dan 2 ni ayirish.

$$2b^{2}+6b-3=0$$

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

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

6 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

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

-8 ni -3 marotabaga ko'paytirish.

$$b=\frac{-6±\sqrt{36+24}}{2\times 2}$$

36 ni 24 ga qo'shish.

$$b=\frac{-6±\sqrt{60}}{2\times 2}$$

60 ning kvadrat ildizini chiqarish.

$$b=\frac{-6±2\sqrt{15}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$b=\frac{-6±2\sqrt{15}}{4}$$

b=\frac{-6±2\sqrt{15}}{4} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{15} ga qo'shish.

$$b=\frac{2\sqrt{15}-6}{4}$$

-6+2\sqrt{15} ni 4 ga bo'lish.

$$b=\frac{\sqrt{15}-3}{2}$$

b=\frac{-6±2\sqrt{15}}{4} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{15} ni ayirish.

$$b=\frac{-2\sqrt{15}-6}{4}$$

-6-2\sqrt{15} ni 4 ga bo'lish.

$$b=\frac{-\sqrt{15}-3}{2}$$

Tenglama yechildi.

$$b=\frac{\sqrt{15}-3}{2} b=\frac{-\sqrt{15}-3}{2}$$

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.

$$2b^{2}+6b-1=2$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$2b^{2}+6b-1-\left(-1\right)=2-\left(-1\right)$$

O‘zidan -1 ayirilsa 0 qoladi.

$$2b^{2}+6b=2-\left(-1\right)$$

2 dan -1 ni ayirish.

$$2b^{2}+6b=3$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2b^{2}+6b}{2}=\frac{3}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$b^{2}+\frac{6}{2}b=\frac{3}{2}$$

6 ni 2 ga bo'lish.

$$b^{2}+3b=\frac{3}{2}$$

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

$$b^{2}+3b+\left(\frac{3}{2}\right)^{2}=\frac{3}{2}+\left(\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.

$$b^{2}+3b+\frac{9}{4}=\frac{3}{2}+\frac{9}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$b^{2}+3b+\frac{9}{4}=\frac{15}{4}$$

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

$$\left(b+\frac{3}{2}\right)^{2}=\frac{15}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b+\frac{3}{2}\right)^{2}}=\sqrt{\frac{15}{4}}$$

Qisqartirish.

$$b+\frac{3}{2}=\frac{\sqrt{15}}{2} b+\frac{3}{2}=-\frac{\sqrt{15}}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$b=\frac{\sqrt{15}-3}{2} b=\frac{-\sqrt{15}-3}{2}$$