128(1+x)(1+x)=200 eching

$$128(1+x)(1+x)=200$$

x uchun yechish

$$x=\frac{1}{4}=0,25$$

$$x = -\frac{9}{4} = -2\frac{1}{4} = -2,25$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$128\left(1+x\right)^{2}=200$$

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

$$128\left(1+2x+x^{2}\right)=200$$

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

$$128+256x+128x^{2}=200$$

Ikkala tarafdan 200 ni ayirish.

$$128+256x+128x^{2}-200=0$$

-72 olish uchun 128 dan 200 ni ayirish.

$$-72+256x+128x^{2}=0$$

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.

$$128x^{2}+256x-72=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 128 ni a, 256 ni b va -72 ni c bilan almashtiring.

$$x=\frac{-256±\sqrt{256^{2}-4\times 128\left(-72\right)}}{2\times 128}$$

256 kvadratini chiqarish.

$$x=\frac{-256±\sqrt{65536-4\times 128\left(-72\right)}}{2\times 128}$$

-4 ni 128 marotabaga ko'paytirish.

$$x=\frac{-256±\sqrt{65536-512\left(-72\right)}}{2\times 128}$$

-512 ni -72 marotabaga ko'paytirish.

$$x=\frac{-256±\sqrt{65536+36864}}{2\times 128}$$

65536 ni 36864 ga qo'shish.

$$x=\frac{-256±\sqrt{102400}}{2\times 128}$$

102400 ning kvadrat ildizini chiqarish.

$$x=\frac{-256±320}{2\times 128}$$

2 ni 128 marotabaga ko'paytirish.

$$x=\frac{-256±320}{256}$$

x=\frac{-256±320}{256} tenglamasini yeching, bunda ± musbat. -256 ni 320 ga qo'shish.

$$x=\frac{64}{256}$$

\frac{64}{256} ulushini 64 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{-256±320}{256} tenglamasini yeching, bunda ± manfiy. -256 dan 320 ni ayirish.

$$x=-\frac{576}{256}$$

\frac{-576}{256} ulushini 64 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{9}{4}$$

Tenglama yechildi.

$$x=\frac{1}{4} x=-\frac{9}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$128\left(1+x\right)^{2}=200$$

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

$$128\left(1+2x+x^{2}\right)=200$$

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

$$128+256x+128x^{2}=200$$

Ikkala tarafdan 128 ni ayirish.

$$256x+128x^{2}=200-128$$

72 olish uchun 200 dan 128 ni ayirish.

$$256x+128x^{2}=72$$

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

$$128x^{2}+256x=72$$

Ikki tarafini 128 ga bo‘ling.

$$\frac{128x^{2}+256x}{128}=\frac{72}{128}$$

128 ga bo'lish 128 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{256}{128}x=\frac{72}{128}$$

256 ni 128 ga bo'lish.

$$x^{2}+2x=\frac{72}{128}$$

\frac{72}{128} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+2x=\frac{9}{16}$$

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.

$$x^{2}+2x+1^{2}=\frac{9}{16}+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=\frac{9}{16}+1$$

\frac{9}{16} ni 1 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\frac{1}{4} x=-\frac{9}{4}$$