25*(1-x)(1-x)=16 eching

$$25 \times ( 1 - x ) ( 1 - x ) = 16$$

x uchun yechish

$$x=\frac{1}{5}=0,2$$

$$x = \frac{9}{5} = 1\frac{4}{5} = 1,8$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(1-x\right)^{2} hosil qilish uchun 1-x va 1-x ni ko'paytirish.

$$25\left(1-x\right)^{2}=16$$

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

$$25\left(1-2x+x^{2}\right)=16$$

25 ga 1-2x+x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$25-50x+25x^{2}=16$$

Ikkala tarafdan 16 ni ayirish.

$$25-50x+25x^{2}-16=0$$

9 olish uchun 25 dan 16 ni ayirish.

$$9-50x+25x^{2}=0$$

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.

$$25x^{2}-50x+9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 25 ni a, -50 ni b va 9 ni c bilan almashtiring.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 25\times 9}}{2\times 25}$$

-50 kvadratini chiqarish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 25\times 9}}{2\times 25}$$

-4 ni 25 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-100\times 9}}{2\times 25}$$

-100 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-900}}{2\times 25}$$

2500 ni -900 ga qo'shish.

$$x=\frac{-\left(-50\right)±\sqrt{1600}}{2\times 25}$$

1600 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-50\right)±40}{2\times 25}$$

-50 ning teskarisi 50 ga teng.

$$x=\frac{50±40}{2\times 25}$$

2 ni 25 marotabaga ko'paytirish.

$$x=\frac{50±40}{50}$$

x=\frac{50±40}{50} tenglamasini yeching, bunda ± musbat. 50 ni 40 ga qo'shish.

$$x=\frac{90}{50}$$

\frac{90}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{9}{5}$$

x=\frac{50±40}{50} tenglamasini yeching, bunda ± manfiy. 50 dan 40 ni ayirish.

$$x=\frac{10}{50}$$

\frac{10}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{5}$$

Tenglama yechildi.

$$x=\frac{9}{5} x=\frac{1}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

\left(1-x\right)^{2} hosil qilish uchun 1-x va 1-x ni ko'paytirish.

$$25\left(1-x\right)^{2}=16$$

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

$$25\left(1-2x+x^{2}\right)=16$$

25 ga 1-2x+x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$25-50x+25x^{2}=16$$

Ikkala tarafdan 25 ni ayirish.

$$-50x+25x^{2}=16-25$$

-9 olish uchun 16 dan 25 ni ayirish.

$$-50x+25x^{2}=-9$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$25x^{2}-50x=-9$$

Ikki tarafini 25 ga bo‘ling.

$$\frac{25x^{2}-50x}{25}=-\frac{9}{25}$$

25 ga bo'lish 25 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{50}{25}\right)x=-\frac{9}{25}$$

-50 ni 25 ga bo'lish.

$$x^{2}-2x=-\frac{9}{25}$$

-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.

$$x^{2}-2x+1=-\frac{9}{25}+1$$

-\frac{9}{25} ni 1 ga qo'shish.

$$x^{2}-2x+1=\frac{16}{25}$$

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.

$$\left(x-1\right)^{2}=\frac{16}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{16}{25}}$$

Qisqartirish.

$$x-1=\frac{4}{5} x-1=-\frac{4}{5}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{9}{5} x=\frac{1}{5}$$