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x^{2}+2x+10=0
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=\frac{-2±\sqrt{2^{2}-4\times 10}}{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 10 ni c bilan almashtiring.
x=\frac{-2±\sqrt{4-4\times 10}}{2}
2 kvadratini chiqarish.
x=\frac{-2±\sqrt{4-40}}{2}
-4 ni 10 marotabaga ko'paytirish.
x=\frac{-2±\sqrt{-36}}{2}
4 ni -40 ga qo'shish.
x=\frac{-2±6i}{2}
-36 ning kvadrat ildizini chiqarish.
x=\frac{-2+6i}{2}
x=\frac{-2±6i}{2} tenglamasini yeching, bunda ± musbat. -2 ni 6i ga qo'shish.
x=-1+3i
-2+6i ni 2 ga bo'lish.
x=\frac{-2-6i}{2}
x=\frac{-2±6i}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 6i ni ayirish.
x=-1-3i
-2-6i ni 2 ga bo'lish.
x=-1+3i x=-1-3i
Tenglama yechildi.
x^{2}+2x+10=0
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+10-10=-10
Tenglamaning ikkala tarafidan 10 ni ayirish.
x^{2}+2x=-10
O‘zidan 10 ayirilsa 0 qoladi.
x^{2}+2x+1^{2}=-10+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=-10+1
1 kvadratini chiqarish.
x^{2}+2x+1=-9
-10 ni 1 ga qo'shish.
\left(x+1\right)^{2}=-9
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{-9}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+1=3i x+1=-3i
Qisqartirish.
x=-1+3i x=-1-3i
Tenglamaning ikkala tarafidan 1 ni ayirish.