(c+7)^2-4(1+7)+3=0 eching

$$( c + 7 ) ^ { 2 } - 4 ( 1 + 7 ) + 3 = 0$$

c uchun yechish

$$c=\sqrt{29}-7\approx -1,614835193$$

$$c=-\left(\sqrt{29}+7\right)\approx -12,385164807$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(c+7\right)^{2} kengaytirilishi uchun ishlating.

$$c^{2}+14c+49-4\left(1+7\right)+3=0$$

8 olish uchun 1 va 7'ni qo'shing.

$$c^{2}+14c+49-4\times 8+3=0$$

32 hosil qilish uchun 4 va 8 ni ko'paytirish.

$$c^{2}+14c+49-32+3=0$$

17 olish uchun 49 dan 32 ni ayirish.

$$c^{2}+14c+17+3=0$$

20 olish uchun 17 va 3'ni qo'shing.

$$c^{2}+14c+20=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 14 ni b va 20 ni c bilan almashtiring.

$$c=\frac{-14±\sqrt{14^{2}-4\times 20}}{2}$$

14 kvadratini chiqarish.

$$c=\frac{-14±\sqrt{196-4\times 20}}{2}$$

-4 ni 20 marotabaga ko'paytirish.

$$c=\frac{-14±\sqrt{196-80}}{2}$$

196 ni -80 ga qo'shish.

$$c=\frac{-14±\sqrt{116}}{2}$$

116 ning kvadrat ildizini chiqarish.

$$c=\frac{-14±2\sqrt{29}}{2}$$

c=\frac{-14±2\sqrt{29}}{2} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{29} ga qo'shish.

$$c=\frac{2\sqrt{29}-14}{2}$$

-14+2\sqrt{29} ni 2 ga bo'lish.

$$c=\sqrt{29}-7$$

c=\frac{-14±2\sqrt{29}}{2} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{29} ni ayirish.

$$c=\frac{-2\sqrt{29}-14}{2}$$

-14-2\sqrt{29} ni 2 ga bo'lish.

$$c=-\sqrt{29}-7$$

Tenglama yechildi.

$$c=\sqrt{29}-7 c=-\sqrt{29}-7$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(c+7\right)^{2} kengaytirilishi uchun ishlating.

$$c^{2}+14c+49-4\left(1+7\right)+3=0$$

8 olish uchun 1 va 7'ni qo'shing.

$$c^{2}+14c+49-4\times 8+3=0$$

32 hosil qilish uchun 4 va 8 ni ko'paytirish.

$$c^{2}+14c+49-32+3=0$$

17 olish uchun 49 dan 32 ni ayirish.

$$c^{2}+14c+17+3=0$$

20 olish uchun 17 va 3'ni qo'shing.

$$c^{2}+14c+20=0$$

Ikkala tarafdan 20 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$c^{2}+14c=-20$$

14 ni bo‘lish, x shartining koeffitsienti, 2 ga 7 olish uchun. Keyin, 7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$c^{2}+14c+7^{2}=-20+7^{2}$$

7 kvadratini chiqarish.

$$c^{2}+14c+49=-20+49$$

-20 ni 49 ga qo'shish.

$$c^{2}+14c+49=29$$

c^{2}+14c+49 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(c+7\right)^{2}=29$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(c+7\right)^{2}}=\sqrt{29}$$

Qisqartirish.

$$c+7=\sqrt{29} c+7=-\sqrt{29}$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$c=\sqrt{29}-7 c=-\sqrt{29}-7$$