x uchun yechish
x=2\sqrt{2}+2\approx 4,828427125
x=2-2\sqrt{2}\approx -0,828427125
Grafik
Baham ko'rish
Klipbordga nusxa olish
x^{2}-4x-4=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\left(-4\right)}}{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 -4 ni c bilan almashtiring.
x=\frac{-\left(-4\right)±\sqrt{16-4\left(-4\right)}}{2}
-4 kvadratini chiqarish.
x=\frac{-\left(-4\right)±\sqrt{16+16}}{2}
-4 ni -4 marotabaga ko'paytirish.
x=\frac{-\left(-4\right)±\sqrt{32}}{2}
16 ni 16 ga qo'shish.
x=\frac{-\left(-4\right)±4\sqrt{2}}{2}
32 ning kvadrat ildizini chiqarish.
x=\frac{4±4\sqrt{2}}{2}
-4 ning teskarisi 4 ga teng.
x=\frac{4\sqrt{2}+4}{2}
x=\frac{4±4\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 4 ni 4\sqrt{2} ga qo'shish.
x=2\sqrt{2}+2
4+4\sqrt{2} ni 2 ga bo'lish.
x=\frac{4-4\sqrt{2}}{2}
x=\frac{4±4\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 4\sqrt{2} ni ayirish.
x=2-2\sqrt{2}
4-4\sqrt{2} ni 2 ga bo'lish.
x=2\sqrt{2}+2 x=2-2\sqrt{2}
Tenglama yechildi.
x^{2}-4x-4=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}-4x-4-\left(-4\right)=-\left(-4\right)
4 ni tenglamaning ikkala tarafiga qo'shish.
x^{2}-4x=-\left(-4\right)
O‘zidan -4 ayirilsa 0 qoladi.
x^{2}-4x=4
0 dan -4 ni ayirish.
x^{2}-4x+\left(-2\right)^{2}=4+\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=4+4
-2 kvadratini chiqarish.
x^{2}-4x+4=8
4 ni 4 ga qo'shish.
\left(x-2\right)^{2}=8
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{8}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-2=2\sqrt{2} x-2=-2\sqrt{2}
Qisqartirish.
x=2\sqrt{2}+2 x=2-2\sqrt{2}
2 ni tenglamaning ikkala tarafiga qo'shish.
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