x^2+8x+2=0 eching

$$x ^ { 2 } + 8 x + 2 = 0$$

x uchun yechish (complex solution)

$$x=\sqrt{14}-4\approx -0,258342613$$

$$x=-\left(\sqrt{14}+4\right)\approx -7,741657387$$

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.

$$x^{2}+8x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 8 ni b va 2 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\times 2}}{2}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\times 2}}{2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64-8}}{2}$$

64 ni -8 ga qo'shish.

$$x=\frac{-8±\sqrt{56}}{2}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{14}}{2}$$

x=\frac{-8±2\sqrt{14}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{14} ga qo'shish.

$$x=\frac{2\sqrt{14}-8}{2}$$

-8+2\sqrt{14} ni 2 ga bo'lish.

$$x=\sqrt{14}-4$$

x=\frac{-8±2\sqrt{14}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{14} ni ayirish.

$$x=\frac{-2\sqrt{14}-8}{2}$$

-8-2\sqrt{14} ni 2 ga bo'lish.

$$x=-\sqrt{14}-4$$

Tenglama yechildi.

$$x=\sqrt{14}-4 x=-\sqrt{14}-4$$

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.

$$x^{2}+8x+2=0$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

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

O‘zidan 2 ayirilsa 0 qoladi.

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

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

$$x^{2}+8x+4^{2}=-2+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=-2+16$$

-2 ni 16 ga qo'shish.

$$x^{2}+8x+16=14$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=14$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{14}$$

Qisqartirish.

$$x+4=\sqrt{14} x+4=-\sqrt{14}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=\sqrt{14}-4 x=-\sqrt{14}-4$$

x uchun yechish

$$x=\sqrt{14}-4\approx -0,258342613$$

$$x=-\sqrt{14}-4\approx -7,741657387$$

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.

$$x^{2}+8x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 8 ni b va 2 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\times 2}}{2}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\times 2}}{2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64-8}}{2}$$

64 ni -8 ga qo'shish.

$$x=\frac{-8±\sqrt{56}}{2}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{14}}{2}$$

x=\frac{-8±2\sqrt{14}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{14} ga qo'shish.

$$x=\frac{2\sqrt{14}-8}{2}$$

-8+2\sqrt{14} ni 2 ga bo'lish.

$$x=\sqrt{14}-4$$

x=\frac{-8±2\sqrt{14}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{14} ni ayirish.

$$x=\frac{-2\sqrt{14}-8}{2}$$

-8-2\sqrt{14} ni 2 ga bo'lish.

$$x=-\sqrt{14}-4$$

Tenglama yechildi.

$$x=\sqrt{14}-4 x=-\sqrt{14}-4$$

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.

$$x^{2}+8x+2=0$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

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

O‘zidan 2 ayirilsa 0 qoladi.

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

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

$$x^{2}+8x+4^{2}=-2+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=-2+16$$

-2 ni 16 ga qo'shish.

$$x^{2}+8x+16=14$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=14$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{14}$$

Qisqartirish.

$$x+4=\sqrt{14} x+4=-\sqrt{14}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=\sqrt{14}-4 x=-\sqrt{14}-4$$