c^2+4c-17=-6 eching

$$c ^ { 2 } + 4 c - 17 = - 6$$

c uchun yechish (complex solution)

$$c=\sqrt{15}-2\approx 1,872983346$$

$$c=-\left(\sqrt{15}+2\right)\approx -5,872983346$$

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.

$$c^{2}+4c-17=-6$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$c^{2}+4c-17-\left(-6\right)=-6-\left(-6\right)$$

O‘zidan -6 ayirilsa 0 qoladi.

$$c^{2}+4c-17-\left(-6\right)=0$$

-17 dan -6 ni ayirish.

$$c^{2}+4c-11=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 4 ni b va -11 ni c bilan almashtiring.

$$c=\frac{-4±\sqrt{4^{2}-4\left(-11\right)}}{2}$$

4 kvadratini chiqarish.

$$c=\frac{-4±\sqrt{16-4\left(-11\right)}}{2}$$

-4 ni -11 marotabaga ko'paytirish.

$$c=\frac{-4±\sqrt{16+44}}{2}$$

16 ni 44 ga qo'shish.

$$c=\frac{-4±\sqrt{60}}{2}$$

60 ning kvadrat ildizini chiqarish.

$$c=\frac{-4±2\sqrt{15}}{2}$$

c=\frac{-4±2\sqrt{15}}{2} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{15} ga qo'shish.

$$c=\frac{2\sqrt{15}-4}{2}$$

-4+2\sqrt{15} ni 2 ga bo'lish.

$$c=\sqrt{15}-2$$

c=\frac{-4±2\sqrt{15}}{2} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{15} ni ayirish.

$$c=\frac{-2\sqrt{15}-4}{2}$$

-4-2\sqrt{15} ni 2 ga bo'lish.

$$c=-\sqrt{15}-2$$

Tenglama yechildi.

$$c=\sqrt{15}-2 c=-\sqrt{15}-2$$

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.

$$c^{2}+4c-17=-6$$

17 ni tenglamaning ikkala tarafiga qo'shish.

$$c^{2}+4c-17-\left(-17\right)=-6-\left(-17\right)$$

O‘zidan -17 ayirilsa 0 qoladi.

$$c^{2}+4c=-6-\left(-17\right)$$

-6 dan -17 ni ayirish.

$$c^{2}+4c=11$$

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.

$$c^{2}+4c+2^{2}=11+2^{2}$$

2 kvadratini chiqarish.

$$c^{2}+4c+4=11+4$$

11 ni 4 ga qo'shish.

$$c^{2}+4c+4=15$$

c^{2}+4c+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.

$$\left(c+2\right)^{2}=15$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(c+2\right)^{2}}=\sqrt{15}$$

Qisqartirish.

$$c+2=\sqrt{15} c+2=-\sqrt{15}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$c=\sqrt{15}-2 c=-\sqrt{15}-2$$

c uchun yechish

$$c=\sqrt{15}-2\approx 1,872983346$$

$$c=-\sqrt{15}-2\approx -5,872983346$$

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.

$$c^{2}+4c-17=-6$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$c^{2}+4c-17-\left(-6\right)=-6-\left(-6\right)$$

O‘zidan -6 ayirilsa 0 qoladi.

$$c^{2}+4c-17-\left(-6\right)=0$$

-17 dan -6 ni ayirish.

$$c^{2}+4c-11=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 4 ni b va -11 ni c bilan almashtiring.

$$c=\frac{-4±\sqrt{4^{2}-4\left(-11\right)}}{2}$$

4 kvadratini chiqarish.

$$c=\frac{-4±\sqrt{16-4\left(-11\right)}}{2}$$

-4 ni -11 marotabaga ko'paytirish.

$$c=\frac{-4±\sqrt{16+44}}{2}$$

16 ni 44 ga qo'shish.

$$c=\frac{-4±\sqrt{60}}{2}$$

60 ning kvadrat ildizini chiqarish.

$$c=\frac{-4±2\sqrt{15}}{2}$$

c=\frac{-4±2\sqrt{15}}{2} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{15} ga qo'shish.

$$c=\frac{2\sqrt{15}-4}{2}$$

-4+2\sqrt{15} ni 2 ga bo'lish.

$$c=\sqrt{15}-2$$

c=\frac{-4±2\sqrt{15}}{2} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{15} ni ayirish.

$$c=\frac{-2\sqrt{15}-4}{2}$$

-4-2\sqrt{15} ni 2 ga bo'lish.

$$c=-\sqrt{15}-2$$

Tenglama yechildi.

$$c=\sqrt{15}-2 c=-\sqrt{15}-2$$

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.

$$c^{2}+4c-17=-6$$

17 ni tenglamaning ikkala tarafiga qo'shish.

$$c^{2}+4c-17-\left(-17\right)=-6-\left(-17\right)$$

O‘zidan -17 ayirilsa 0 qoladi.

$$c^{2}+4c=-6-\left(-17\right)$$

-6 dan -17 ni ayirish.

$$c^{2}+4c=11$$

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.

$$c^{2}+4c+2^{2}=11+2^{2}$$

2 kvadratini chiqarish.

$$c^{2}+4c+4=11+4$$

11 ni 4 ga qo'shish.

$$c^{2}+4c+4=15$$

c^{2}+4c+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.

$$\left(c+2\right)^{2}=15$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(c+2\right)^{2}}=\sqrt{15}$$

Qisqartirish.

$$c+2=\sqrt{15} c+2=-\sqrt{15}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$c=\sqrt{15}-2 c=-\sqrt{15}-2$$