x^2+3+8x=2x-1 eching

$$x ^ { 2 } + 3 + 8 x = 2 x - 1$$

x uchun yechish (complex solution)

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

$$x=-\left(\sqrt{5}+3\right)\approx -5,236067977$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

$$x^{2}+3+8x-2x=-1$$

6x ni olish uchun 8x va -2x ni birlashtirish.

$$x^{2}+3+6x=-1$$

1 ni ikki tarafga qo’shing.

$$x^{2}+3+6x+1=0$$

4 olish uchun 3 va 1'ni qo'shing.

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

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.

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

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.

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

6 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-16}}{2}$$

36 ni -16 ga qo'shish.

$$x=\frac{-6±\sqrt{20}}{2}$$

20 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{5}}{2}$$

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

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

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

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

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

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

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

$$x^{2}+3+8x-2x=-1$$

6x ni olish uchun 8x va -2x ni birlashtirish.

$$x^{2}+3+6x=-1$$

Ikkala tarafdan 3 ni ayirish.

$$x^{2}+6x=-1-3$$

-4 olish uchun -1 dan 3 ni ayirish.

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

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.

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

3 kvadratini chiqarish.

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

-4 ni 9 ga qo'shish.

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

x^{2}+6x+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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

x uchun yechish

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

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

$$x^{2}+3+8x-2x=-1$$

6x ni olish uchun 8x va -2x ni birlashtirish.

$$x^{2}+3+6x=-1$$

1 ni ikki tarafga qo’shing.

$$x^{2}+3+6x+1=0$$

4 olish uchun 3 va 1'ni qo'shing.

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

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.

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

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.

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

6 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-16}}{2}$$

36 ni -16 ga qo'shish.

$$x=\frac{-6±\sqrt{20}}{2}$$

20 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{5}}{2}$$

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

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

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

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

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

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

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

$$x^{2}+3+8x-2x=-1$$

6x ni olish uchun 8x va -2x ni birlashtirish.

$$x^{2}+3+6x=-1$$

Ikkala tarafdan 3 ni ayirish.

$$x^{2}+6x=-1-3$$

-4 olish uchun -1 dan 3 ni ayirish.

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

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.

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

3 kvadratini chiqarish.

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

-4 ni 9 ga qo'shish.

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

x^{2}+6x+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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