(x-2)^2-4x+2=0 eching

$$( x - 2 ) ^ { 2 } - 4 x + 2 = 0$$

x uchun yechish

$$x=\sqrt{10}+4\approx 7,16227766$$

$$x=4-\sqrt{10}\approx 0,83772234$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-4x+4-4x+2=0$$

-8x ni olish uchun -4x va -4x ni birlashtirish.

$$x^{2}-8x+4+2=0$$

6 olish uchun 4 va 2'ni qo'shing.

$$x^{2}-8x+6=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 6}}{2}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-24}}{2}$$

64 ni -24 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{40}}{2}$$

40 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±2\sqrt{10}}{2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±2\sqrt{10}}{2}$$

x=\frac{8±2\sqrt{10}}{2} tenglamasini yeching, bunda ± musbat. 8 ni 2\sqrt{10} ga qo'shish.

$$x=\frac{2\sqrt{10}+8}{2}$$

8+2\sqrt{10} ni 2 ga bo'lish.

$$x=\sqrt{10}+4$$

x=\frac{8±2\sqrt{10}}{2} tenglamasini yeching, bunda ± manfiy. 8 dan 2\sqrt{10} ni ayirish.

$$x=\frac{8-2\sqrt{10}}{2}$$

8-2\sqrt{10} ni 2 ga bo'lish.

$$x=4-\sqrt{10}$$

Tenglama yechildi.

$$x=\sqrt{10}+4 x=4-\sqrt{10}$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-4x+4-4x+2=0$$

-8x ni olish uchun -4x va -4x ni birlashtirish.

$$x^{2}-8x+4+2=0$$

6 olish uchun 4 va 2'ni qo'shing.

$$x^{2}-8x+6=0$$

Ikkala tarafdan 6 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-8x=-6$$

-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.

$$x^{2}-8x+\left(-4\right)^{2}=-6+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$x^{2}-8x+16=-6+16$$

-6 ni 16 ga qo'shish.

$$x^{2}-8x+16=10$$

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.

$$\left(x-4\right)^{2}=10$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{10}$$

Qisqartirish.

$$x-4=\sqrt{10} x-4=-\sqrt{10}$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{10}+4 x=4-\sqrt{10}$$