x^2+8x=3 eching

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

x uchun yechish (complex solution)

$$x=\sqrt{19}-4\approx 0,358898944$$

$$x=-\left(\sqrt{19}+4\right)\approx -8,358898944$$

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.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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

O‘zidan 3 ayirilsa 0 qoladi.

$$x^{2}+8x-3=0$$

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 -3 ni c bilan almashtiring.

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

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-3\right)}}{2}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+12}}{2}$$

64 ni 12 ga qo'shish.

$$x=\frac{-8±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{19}}{2}$$

x=\frac{-8±2\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}-8}{2}$$

-8+2\sqrt{19} ni 2 ga bo'lish.

$$x=\sqrt{19}-4$$

x=\frac{-8±2\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{19} ni ayirish.

$$x=\frac{-2\sqrt{19}-8}{2}$$

-8-2\sqrt{19} ni 2 ga bo'lish.

$$x=-\sqrt{19}-4$$

Tenglama yechildi.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$

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.

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

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.

$$x^{2}+8x+4^{2}=3+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=3+16$$

3 ni 16 ga qo'shish.

$$x^{2}+8x+16=19$$

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.

$$\left(x+4\right)^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{19}$$

Qisqartirish.

$$x+4=\sqrt{19} x+4=-\sqrt{19}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$

x uchun yechish

$$x=\sqrt{19}-4\approx 0,358898944$$

$$x=-\sqrt{19}-4\approx -8,358898944$$

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.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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

O‘zidan 3 ayirilsa 0 qoladi.

$$x^{2}+8x-3=0$$

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 -3 ni c bilan almashtiring.

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

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-3\right)}}{2}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+12}}{2}$$

64 ni 12 ga qo'shish.

$$x=\frac{-8±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{19}}{2}$$

x=\frac{-8±2\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}-8}{2}$$

-8+2\sqrt{19} ni 2 ga bo'lish.

$$x=\sqrt{19}-4$$

x=\frac{-8±2\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{19} ni ayirish.

$$x=\frac{-2\sqrt{19}-8}{2}$$

-8-2\sqrt{19} ni 2 ga bo'lish.

$$x=-\sqrt{19}-4$$

Tenglama yechildi.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$

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.

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

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.

$$x^{2}+8x+4^{2}=3+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=3+16$$

3 ni 16 ga qo'shish.

$$x^{2}+8x+16=19$$

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.

$$\left(x+4\right)^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{19}$$

Qisqartirish.

$$x+4=\sqrt{19} x+4=-\sqrt{19}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=\sqrt{19}-4 x=-\sqrt{19}-4$$