x uchun yechish (complex solution)
x=-1+i
x=-1-i
Grafik
Baham ko'rish
Klipbordga nusxa olish
x^{2}+2x+3=1
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}+2x+3-1=1-1
Tenglamaning ikkala tarafidan 1 ni ayirish.
x^{2}+2x+3-1=0
O‘zidan 1 ayirilsa 0 qoladi.
x^{2}+2x+2=0
3 dan 1 ni ayirish.
x=\frac{-2±\sqrt{2^{2}-4\times 2}}{2}
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 2 ni c bilan almashtiring.
x=\frac{-2±\sqrt{4-4\times 2}}{2}
2 kvadratini chiqarish.
x=\frac{-2±\sqrt{4-8}}{2}
-4 ni 2 marotabaga ko'paytirish.
x=\frac{-2±\sqrt{-4}}{2}
4 ni -8 ga qo'shish.
x=\frac{-2±2i}{2}
-4 ning kvadrat ildizini chiqarish.
x=\frac{-2+2i}{2}
x=\frac{-2±2i}{2} tenglamasini yeching, bunda ± musbat. -2 ni 2i ga qo'shish.
x=-1+i
-2+2i ni 2 ga bo'lish.
x=\frac{-2-2i}{2}
x=\frac{-2±2i}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 2i ni ayirish.
x=-1-i
-2-2i ni 2 ga bo'lish.
x=-1+i x=-1-i
Tenglama yechildi.
x^{2}+2x+3=1
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
x^{2}+2x+3-3=1-3
Tenglamaning ikkala tarafidan 3 ni ayirish.
x^{2}+2x=1-3
O‘zidan 3 ayirilsa 0 qoladi.
x^{2}+2x=-2
1 dan 3 ni ayirish.
x^{2}+2x+1^{2}=-2+1^{2}
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.
x^{2}+2x+1=-2+1
1 kvadratini chiqarish.
x^{2}+2x+1=-1
-2 ni 1 ga qo'shish.
\left(x+1\right)^{2}=-1
x^{2}+2x+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.
\sqrt{\left(x+1\right)^{2}}=\sqrt{-1}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+1=i x+1=-i
Qisqartirish.
x=-1+i x=-1-i
Tenglamaning ikkala tarafidan 1 ni ayirish.
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