a^2+6a+4=0 eching

$$a ^ { 2 } + 6 a + 4 = 0$$

a uchun yechish

$$a=\sqrt{5}-3\approx -0,763932023$$

$$a=-\sqrt{5}-3\approx -5,236067977$$

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.

$$a^{2}+6a+4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 6 ni b va 4 ni c bilan almashtiring.

$$a=\frac{-6±\sqrt{6^{2}-4\times 4}}{2}$$

6 kvadratini chiqarish.

$$a=\frac{-6±\sqrt{36-4\times 4}}{2}$$

-4 ni 4 marotabaga ko'paytirish.

$$a=\frac{-6±\sqrt{36-16}}{2}$$

36 ni -16 ga qo'shish.

$$a=\frac{-6±\sqrt{20}}{2}$$

20 ning kvadrat ildizini chiqarish.

$$a=\frac{-6±2\sqrt{5}}{2}$$

a=\frac{-6±2\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{5} ga qo'shish.

$$a=\frac{2\sqrt{5}-6}{2}$$

-6+2\sqrt{5} ni 2 ga bo'lish.

$$a=\sqrt{5}-3$$

a=\frac{-6±2\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{5} ni ayirish.

$$a=\frac{-2\sqrt{5}-6}{2}$$

-6-2\sqrt{5} ni 2 ga bo'lish.

$$a=-\sqrt{5}-3$$

Tenglama yechildi.

$$a=\sqrt{5}-3 a=-\sqrt{5}-3$$

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.

$$a^{2}+6a+4=0$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$a^{2}+6a+4-4=-4$$

O‘zidan 4 ayirilsa 0 qoladi.

$$a^{2}+6a=-4$$

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

$$a^{2}+6a+3^{2}=-4+3^{2}$$

3 kvadratini chiqarish.

$$a^{2}+6a+9=-4+9$$

-4 ni 9 ga qo'shish.

$$a^{2}+6a+9=5$$

a^{2}+6a+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a+3\right)^{2}=5$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+3\right)^{2}}=\sqrt{5}$$

Qisqartirish.

$$a+3=\sqrt{5} a+3=-\sqrt{5}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$a=\sqrt{5}-3 a=-\sqrt{5}-3$$