b^2+2b=-20 eching

$$b ^ { 2 } + 2 b = - 20$$

b uchun yechish

$$b=-1+\sqrt{19}i\approx -1+4,358898944i$$

$$b=-\sqrt{19}i-1\approx -1-4,358898944i$$

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.

$$b^{2}+2b=-20$$

20 ni tenglamaning ikkala tarafiga qo'shish.

$$b^{2}+2b-\left(-20\right)=-20-\left(-20\right)$$

O‘zidan -20 ayirilsa 0 qoladi.

$$b^{2}+2b-\left(-20\right)=0$$

0 dan -20 ni ayirish.

$$b^{2}+2b+20=0$$

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

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

2 kvadratini chiqarish.

$$b=\frac{-2±\sqrt{4-4\times 20}}{2}$$

-4 ni 20 marotabaga ko'paytirish.

$$b=\frac{-2±\sqrt{4-80}}{2}$$

4 ni -80 ga qo'shish.

$$b=\frac{-2±\sqrt{-76}}{2}$$

-76 ning kvadrat ildizini chiqarish.

$$b=\frac{-2±2\sqrt{19}i}{2}$$

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

$$b=\frac{-2+2\sqrt{19}i}{2}$$

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

$$b=-1+\sqrt{19}i$$

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

$$b=\frac{-2\sqrt{19}i-2}{2}$$

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

$$b=-\sqrt{19}i-1$$

Tenglama yechildi.

$$b=-1+\sqrt{19}i b=-\sqrt{19}i-1$$

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.

$$b^{2}+2b=-20$$

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$b^{2}+2b+1^{2}=-20+1^{2}$$

1 kvadratini chiqarish.

$$b^{2}+2b+1=-20+1$$

-20 ni 1 ga qo'shish.

$$b^{2}+2b+1=-19$$

b^{2}+2b+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(b+1\right)^{2}=-19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b+1\right)^{2}}=\sqrt{-19}$$

Qisqartirish.

$$b+1=\sqrt{19}i b+1=-\sqrt{19}i$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$b=-1+\sqrt{19}i b=-\sqrt{19}i-1$$