-(x-1)^2=-2x+1 eching

$$- ( x - 1 ) ^ { 2 } = - 2 x + 1$$

x uchun yechish

$$x=\sqrt{2}+2\approx 3,414213562$$

$$x=2-\sqrt{2}\approx 0,585786438$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

$$-\left(x^{2}-2x+1\right)=-2x+1$$

x^{2}-2x+1 teskarisini topish uchun har birining teskarisini toping.

$$-x^{2}+2x-1=-2x+1$$

2x ni ikki tarafga qo’shing.

$$-x^{2}+2x-1+2x=1$$

4x ni olish uchun 2x va 2x ni birlashtirish.

$$-x^{2}+4x-1=1$$

Ikkala tarafdan 1 ni ayirish.

$$-x^{2}+4x-1-1=0$$

-2 olish uchun -1 dan 1 ni ayirish.

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

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 -2 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+4\left(-2\right)}}{2\left(-1\right)}$$

4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-8}}{2\left(-1\right)}$$

16 ni -8 ga qo'shish.

$$x=\frac{-4±\sqrt{8}}{2\left(-1\right)}$$

8 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{2}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±2\sqrt{2}}{-2}$$

x=\frac{-4±2\sqrt{2}}{-2} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{2} ga qo'shish.

$$x=\frac{2\sqrt{2}-4}{-2}$$

-4+2\sqrt{2} ni -2 ga bo'lish.

$$x=2-\sqrt{2}$$

x=\frac{-4±2\sqrt{2}}{-2} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{2} ni ayirish.

$$x=\frac{-2\sqrt{2}-4}{-2}$$

-4-2\sqrt{2} ni -2 ga bo'lish.

$$x=\sqrt{2}+2$$

Tenglama yechildi.

$$x=2-\sqrt{2} x=\sqrt{2}+2$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

$$-\left(x^{2}-2x+1\right)=-2x+1$$

x^{2}-2x+1 teskarisini topish uchun har birining teskarisini toping.

$$-x^{2}+2x-1=-2x+1$$

2x ni ikki tarafga qo’shing.

$$-x^{2}+2x-1+2x=1$$

4x ni olish uchun 2x va 2x ni birlashtirish.

$$-x^{2}+4x-1=1$$

1 ni ikki tarafga qo’shing.

$$-x^{2}+4x=1+1$$

2 olish uchun 1 va 1'ni qo'shing.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+4x}{-1}=\frac{2}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{4}{-1}x=\frac{2}{-1}$$

4 ni -1 ga bo'lish.

$$x^{2}-4x=\frac{2}{-1}$$

2 ni -1 ga bo'lish.

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

-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.

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

-2 kvadratini chiqarish.

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

-2 ni 4 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-2=\sqrt{2} x-2=-\sqrt{2}$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{2}+2 x=2-\sqrt{2}$$