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x^{2}+1-4x=0
Ikkala tarafdan 4x ni ayirish.
x^{2}-4x+1=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(-4\right)±\sqrt{\left(-4\right)^{2}-4}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4 ni b va 1 ni c bilan almashtiring.
x=\frac{-\left(-4\right)±\sqrt{16-4}}{2}
-4 kvadratini chiqarish.
x=\frac{-\left(-4\right)±\sqrt{12}}{2}
16 ni -4 ga qo'shish.
x=\frac{-\left(-4\right)±2\sqrt{3}}{2}
12 ning kvadrat ildizini chiqarish.
x=\frac{4±2\sqrt{3}}{2}
-4 ning teskarisi 4 ga teng.
x=\frac{2\sqrt{3}+4}{2}
x=\frac{4±2\sqrt{3}}{2} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{3} ga qo'shish.
x=\sqrt{3}+2
4+2\sqrt{3} ni 2 ga bo'lish.
x=\frac{4-2\sqrt{3}}{2}
x=\frac{4±2\sqrt{3}}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{3} ni ayirish.
x=2-\sqrt{3}
4-2\sqrt{3} ni 2 ga bo'lish.
x=\sqrt{3}+2 x=2-\sqrt{3}
Tenglama yechildi.
x^{2}+1-4x=0
Ikkala tarafdan 4x ni ayirish.
x^{2}-4x=-1
Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.
x^{2}-4x+\left(-2\right)^{2}=-1+\left(-2\right)^{2}
-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}-4x+4=-1+4
-2 kvadratini chiqarish.
x^{2}-4x+4=3
-1 ni 4 ga qo'shish.
\left(x-2\right)^{2}=3
x^{2}-4x+4 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-2\right)^{2}}=\sqrt{3}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-2=\sqrt{3} x-2=-\sqrt{3}
Qisqartirish.
x=\sqrt{3}+2 x=2-\sqrt{3}
2 ni tenglamaning ikkala tarafiga qo'shish.