(x-1)(x-2)+(x-2)=25 eching

$$(x-1)(x-2)+(x-2)=25$$

x uchun yechish

$$x=\sqrt{26}+1\approx 6,099019514$$

$$x=1-\sqrt{26}\approx -4,099019514$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-1 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-3x+2+x-2=25$$

-2x ni olish uchun -3x va x ni birlashtirish.

$$x^{2}-2x+2-2=25$$

0 olish uchun 2 dan 2 ni ayirish.

$$x^{2}-2x=25$$

Ikkala tarafdan 25 ni ayirish.

$$x^{2}-2x-25=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va -25 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-25\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-25\right)}}{2}$$

-4 ni -25 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+100}}{2}$$

4 ni 100 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{104}}{2}$$

104 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{26}}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{26}}{2}$$

x=\frac{2±2\sqrt{26}}{2} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{26} ga qo'shish.

$$x=\frac{2\sqrt{26}+2}{2}$$

2+2\sqrt{26} ni 2 ga bo'lish.

$$x=\sqrt{26}+1$$

x=\frac{2±2\sqrt{26}}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{26} ni ayirish.

$$x=\frac{2-2\sqrt{26}}{2}$$

2-2\sqrt{26} ni 2 ga bo'lish.

$$x=1-\sqrt{26}$$

Tenglama yechildi.

$$x=\sqrt{26}+1 x=1-\sqrt{26}$$

Kvadratni yakunlash bo'yicha qadamlar

x-1 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-3x+2+x-2=25$$

-2x ni olish uchun -3x va x ni birlashtirish.

$$x^{2}-2x+2-2=25$$

0 olish uchun 2 dan 2 ni ayirish.

$$x^{2}-2x=25$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2x+1=25+1$$

25 ni 1 ga qo'shish.

$$x^{2}-2x+1=26$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=26$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{26}$$

Qisqartirish.

$$x-1=\sqrt{26} x-1=-\sqrt{26}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{26}+1 x=1-\sqrt{26}$$