x^2-6x+10=0 eching

$${ x }^{ 2 } -6x+10 = 0$$

x uchun yechish (complex solution)

$$x=3+i$$

$$x=3-i$$

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.

$$x^{2}-6x+10=0$$

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 10 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 10}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 10}}{2}$$

-4 ni 10 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-40}}{2}$$

36 ni -40 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{-4}}{2}$$

-4 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2i}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2i}{2}$$

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

$$x=\frac{6+2i}{2}$$

6+2i ni 2 ga bo'lish.

$$x=3+i$$

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

$$x=\frac{6-2i}{2}$$

6-2i ni 2 ga bo'lish.

$$x=3-i$$

Tenglama yechildi.

$$x=3+i x=3-i$$

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.

$$x^{2}-6x+10=0$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$x^{2}-6x+10-10=-10$$

O‘zidan 10 ayirilsa 0 qoladi.

$$x^{2}-6x=-10$$

-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.

$$x^{2}-6x+\left(-3\right)^{2}=-10+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=-10+9$$

-10 ni 9 ga qo'shish.

$$x^{2}-6x+9=-1$$

x^{2}-6x+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.

$$\left(x-3\right)^{2}=-1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{-1}$$

Qisqartirish.

$$x-3=i x-3=-i$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=3+i x=3-i$$