z^2-6z+34=0 eching

$$z ^ { 2 } - 6 z + 34 = 0$$

z uchun yechish

$$z=3+5i$$

$$z=3-5i$$

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.

$$z^{2}-6z+34=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va 34 ni c bilan almashtiring.

$$z=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 34}}{2}$$

-6 kvadratini chiqarish.

$$z=\frac{-\left(-6\right)±\sqrt{36-4\times 34}}{2}$$

-4 ni 34 marotabaga ko'paytirish.

$$z=\frac{-\left(-6\right)±\sqrt{36-136}}{2}$$

36 ni -136 ga qo'shish.

$$z=\frac{-\left(-6\right)±\sqrt{-100}}{2}$$

-100 ning kvadrat ildizini chiqarish.

$$z=\frac{-\left(-6\right)±10i}{2}$$

-6 ning teskarisi 6 ga teng.

$$z=\frac{6±10i}{2}$$

z=\frac{6±10i}{2} tenglamasini yeching, bunda ± musbat. 6 ni 10i ga qo'shish.

$$z=\frac{6+10i}{2}$$

6+10i ni 2 ga bo'lish.

$$z=3+5i$$

z=\frac{6±10i}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 10i ni ayirish.

$$z=\frac{6-10i}{2}$$

6-10i ni 2 ga bo'lish.

$$z=3-5i$$

Tenglama yechildi.

$$z=3+5i z=3-5i$$

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.

$$z^{2}-6z+34=0$$

Tenglamaning ikkala tarafidan 34 ni ayirish.

$$z^{2}-6z+34-34=-34$$

O‘zidan 34 ayirilsa 0 qoladi.

$$z^{2}-6z=-34$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$z^{2}-6z+\left(-3\right)^{2}=-34+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$z^{2}-6z+9=-34+9$$

-34 ni 9 ga qo'shish.

$$z^{2}-6z+9=-25$$

z^{2}-6z+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(z-3\right)^{2}=-25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(z-3\right)^{2}}=\sqrt{-25}$$

Qisqartirish.

$$z-3=5i z-3=-5i$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$z=3+5i z=3-5i$$