2a^2-8a-5=0 eching

$$2 a ^ { 2 } - 8 a - 5 = 0$$

a uchun yechish

$$a=\frac{\sqrt{26}}{2}+2\approx 4,549509757$$

$$a=-\frac{\sqrt{26}}{2}+2\approx -0,549509757$$

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.

$$2a^{2}-8a-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -8 ni b va -5 ni c bilan almashtiring.

$$a=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-5\right)}}{2\times 2}$$

-8 kvadratini chiqarish.

$$a=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-5\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$a=\frac{-\left(-8\right)±\sqrt{64-8\left(-5\right)}}{2\times 2}$$

-8 ni -5 marotabaga ko'paytirish.

$$a=\frac{-\left(-8\right)±\sqrt{64+40}}{2\times 2}$$

64 ni 40 ga qo'shish.

$$a=\frac{-\left(-8\right)±\sqrt{104}}{2\times 2}$$

104 ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-8\right)±2\sqrt{26}}{2\times 2}$$

-8 ning teskarisi 8 ga teng.

$$a=\frac{8±2\sqrt{26}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$a=\frac{8±2\sqrt{26}}{4}$$

a=\frac{8±2\sqrt{26}}{4} tenglamasini yeching, bunda ± musbat. 8 ni 2\sqrt{26} ga qo'shish.

$$a=\frac{2\sqrt{26}+8}{4}$$

8+2\sqrt{26} ni 4 ga bo'lish.

$$a=\frac{\sqrt{26}}{2}+2$$

a=\frac{8±2\sqrt{26}}{4} tenglamasini yeching, bunda ± manfiy. 8 dan 2\sqrt{26} ni ayirish.

$$a=\frac{8-2\sqrt{26}}{4}$$

8-2\sqrt{26} ni 4 ga bo'lish.

$$a=-\frac{\sqrt{26}}{2}+2$$

Tenglama yechildi.

$$a=\frac{\sqrt{26}}{2}+2 a=-\frac{\sqrt{26}}{2}+2$$

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.

$$2a^{2}-8a-5=0$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$2a^{2}-8a-5-\left(-5\right)=-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$2a^{2}-8a=-\left(-5\right)$$

0 dan -5 ni ayirish.

$$2a^{2}-8a=5$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2a^{2}-8a}{2}=\frac{5}{2}$$

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

$$a^{2}+\left(-\frac{8}{2}\right)a=\frac{5}{2}$$

-8 ni 2 ga bo'lish.

$$a^{2}-4a=\frac{5}{2}$$

-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-4a+\left(-2\right)^{2}=\frac{5}{2}+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$a^{2}-4a+4=\frac{5}{2}+4$$

\frac{5}{2} ni 4 ga qo'shish.

$$a^{2}-4a+4=\frac{13}{2}$$

a^{2}-4a+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.

$$\left(a-2\right)^{2}=\frac{13}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-2\right)^{2}}=\sqrt{\frac{13}{2}}$$

Qisqartirish.

$$a-2=\frac{\sqrt{26}}{2} a-2=-\frac{\sqrt{26}}{2}$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$a=\frac{\sqrt{26}}{2}+2 a=-\frac{\sqrt{26}}{2}+2$$