b^2-4b+13=0 eching

$$b ^ { 2 } - 4 b + 13 = 0$$

b uchun yechish

$$b=2+3i$$

$$b=2-3i$$

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.

$$b^{2}-4b+13=0$$

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 13 ni c bilan almashtiring.

$$b=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 13}}{2}$$

-4 kvadratini chiqarish.

$$b=\frac{-\left(-4\right)±\sqrt{16-4\times 13}}{2}$$

-4 ni 13 marotabaga ko'paytirish.

$$b=\frac{-\left(-4\right)±\sqrt{16-52}}{2}$$

16 ni -52 ga qo'shish.

$$b=\frac{-\left(-4\right)±\sqrt{-36}}{2}$$

-36 ning kvadrat ildizini chiqarish.

$$b=\frac{-\left(-4\right)±6i}{2}$$

-4 ning teskarisi 4 ga teng.

$$b=\frac{4±6i}{2}$$

b=\frac{4±6i}{2} tenglamasini yeching, bunda ± musbat. 4 ni 6i ga qo'shish.

$$b=\frac{4+6i}{2}$$

4+6i ni 2 ga bo'lish.

$$b=2+3i$$

b=\frac{4±6i}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 6i ni ayirish.

$$b=\frac{4-6i}{2}$$

4-6i ni 2 ga bo'lish.

$$b=2-3i$$

Tenglama yechildi.

$$b=2+3i b=2-3i$$

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.

$$b^{2}-4b+13=0$$

Tenglamaning ikkala tarafidan 13 ni ayirish.

$$b^{2}-4b+13-13=-13$$

O‘zidan 13 ayirilsa 0 qoladi.

$$b^{2}-4b=-13$$

-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.

$$b^{2}-4b+\left(-2\right)^{2}=-13+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$b^{2}-4b+4=-13+4$$

-13 ni 4 ga qo'shish.

$$b^{2}-4b+4=-9$$

b^{2}-4b+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.

$$\left(b-2\right)^{2}=-9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b-2\right)^{2}}=\sqrt{-9}$$

Qisqartirish.

$$b-2=3i b-2=-3i$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$b=2+3i b=2-3i$$