-2a^2-2a-3=-4a^2 eching

$$- 2 a ^ { 2 } - 2 a - 3 = - 4 a ^ { 2 }$$

a uchun yechish

$$a = \frac{\sqrt{7} + 1}{2} \approx 1,822875656$$

$$a=\frac{1-\sqrt{7}}{2}\approx -0,822875656$$

Kvadrat tenglamalaridan foydalanish qoidalari

4a^{2} ni ikki tarafga qo’shing.

$$-2a^{2}-2a-3+4a^{2}=0$$

2a^{2} ni olish uchun -2a^{2} va 4a^{2} ni birlashtirish.

$$2a^{2}-2a-3=0$$

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

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

-2 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

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

-8 ni -3 marotabaga ko'paytirish.

$$a=\frac{-\left(-2\right)±\sqrt{4+24}}{2\times 2}$$

4 ni 24 ga qo'shish.

$$a=\frac{-\left(-2\right)±\sqrt{28}}{2\times 2}$$

28 ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-2\right)±2\sqrt{7}}{2\times 2}$$

-2 ning teskarisi 2 ga teng.

$$a=\frac{2±2\sqrt{7}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$a=\frac{2±2\sqrt{7}}{4}$$

a=\frac{2±2\sqrt{7}}{4} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{7} ga qo'shish.

$$a=\frac{2\sqrt{7}+2}{4}$$

2+2\sqrt{7} ni 4 ga bo'lish.

$$a=\frac{\sqrt{7}+1}{2}$$

a=\frac{2±2\sqrt{7}}{4} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{7} ni ayirish.

$$a=\frac{2-2\sqrt{7}}{4}$$

2-2\sqrt{7} ni 4 ga bo'lish.

$$a=\frac{1-\sqrt{7}}{2}$$

Tenglama yechildi.

$$a=\frac{\sqrt{7}+1}{2} a=\frac{1-\sqrt{7}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

4a^{2} ni ikki tarafga qo’shing.

$$-2a^{2}-2a-3+4a^{2}=0$$

2a^{2} ni olish uchun -2a^{2} va 4a^{2} ni birlashtirish.

$$2a^{2}-2a-3=0$$

3 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2a^{2}-2a=3$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2a^{2}-2a}{2}=\frac{3}{2}$$

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

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

-2 ni 2 ga bo'lish.

$$a^{2}-a=\frac{3}{2}$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-a+\left(-\frac{1}{2}\right)^{2}=\frac{3}{2}+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$a^{2}-a+\frac{1}{4}=\frac{3}{2}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$a^{2}-a+\frac{1}{4}=\frac{7}{4}$$

a^{2}-a+\frac{1}{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.

$$\left(a-\frac{1}{2}\right)^{2}=\frac{7}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-\frac{1}{2}\right)^{2}}=\sqrt{\frac{7}{4}}$$

Qisqartirish.

$$a-\frac{1}{2}=\frac{\sqrt{7}}{2} a-\frac{1}{2}=-\frac{\sqrt{7}}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$a=\frac{\sqrt{7}+1}{2} a=\frac{1-\sqrt{7}}{2}$$