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x^{2}-8x+6=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{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 6}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -8 ni b va 6 ni c bilan almashtiring.
x=\frac{-\left(-8\right)±\sqrt{64-4\times 6}}{2}
-8 kvadratini chiqarish.
x=\frac{-\left(-8\right)±\sqrt{64-24}}{2}
-4 ni 6 marotabaga ko'paytirish.
x=\frac{-\left(-8\right)±\sqrt{40}}{2}
64 ni -24 ga qo'shish.
x=\frac{-\left(-8\right)±2\sqrt{10}}{2}
40 ning kvadrat ildizini chiqarish.
x=\frac{8±2\sqrt{10}}{2}
-8 ning teskarisi 8 ga teng.
x=\frac{2\sqrt{10}+8}{2}
x=\frac{8±2\sqrt{10}}{2} tenglamasini yeching, bunda ± musbat. 8 ni 2\sqrt{10} ga qo'shish.
x=\sqrt{10}+4
8+2\sqrt{10} ni 2 ga bo'lish.
x=\frac{8-2\sqrt{10}}{2}
x=\frac{8±2\sqrt{10}}{2} tenglamasini yeching, bunda ± manfiy. 8 dan 2\sqrt{10} ni ayirish.
x=4-\sqrt{10}
8-2\sqrt{10} ni 2 ga bo'lish.
x=\sqrt{10}+4 x=4-\sqrt{10}
Tenglama yechildi.
x^{2}-8x+6=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}-8x+6-6=-6
Tenglamaning ikkala tarafidan 6 ni ayirish.
x^{2}-8x=-6
O‘zidan 6 ayirilsa 0 qoladi.
x^{2}-8x+\left(-4\right)^{2}=-6+\left(-4\right)^{2}
-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}-8x+16=-6+16
-4 kvadratini chiqarish.
x^{2}-8x+16=10
-6 ni 16 ga qo'shish.
\left(x-4\right)^{2}=10
x^{2}-8x+16 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-4\right)^{2}}=\sqrt{10}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-4=\sqrt{10} x-4=-\sqrt{10}
Qisqartirish.
x=\sqrt{10}+4 x=4-\sqrt{10}
4 ni tenglamaning ikkala tarafiga qo'shish.