(48-x)(52-x)=2300 eching

$$(48-x)(52-x)=2300$$

x uchun yechish

$$x=98$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

48-x ga 52-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2496-100x+x^{2}=2300$$

Ikkala tarafdan 2300 ni ayirish.

$$2496-100x+x^{2}-2300=0$$

196 olish uchun 2496 dan 2300 ni ayirish.

$$196-100x+x^{2}=0$$

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.

$$x^{2}-100x+196=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -100 ni b va 196 ni c bilan almashtiring.

$$x=\frac{-\left(-100\right)±\sqrt{\left(-100\right)^{2}-4\times 196}}{2}$$

-100 kvadratini chiqarish.

$$x=\frac{-\left(-100\right)±\sqrt{10000-4\times 196}}{2}$$

-4 ni 196 marotabaga ko'paytirish.

$$x=\frac{-\left(-100\right)±\sqrt{10000-784}}{2}$$

10000 ni -784 ga qo'shish.

$$x=\frac{-\left(-100\right)±\sqrt{9216}}{2}$$

9216 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-100\right)±96}{2}$$

-100 ning teskarisi 100 ga teng.

$$x=\frac{100±96}{2}$$

x=\frac{100±96}{2} tenglamasini yeching, bunda ± musbat. 100 ni 96 ga qo'shish.

$$x=\frac{196}{2}$$

196 ni 2 ga bo'lish.

$$x=98$$

x=\frac{100±96}{2} tenglamasini yeching, bunda ± manfiy. 100 dan 96 ni ayirish.

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

4 ni 2 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=98 x=2$$

Kvadratni yakunlash bo'yicha qadamlar

48-x ga 52-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2496-100x+x^{2}=2300$$

Ikkala tarafdan 2496 ni ayirish.

$$-100x+x^{2}=2300-2496$$

-196 olish uchun 2300 dan 2496 ni ayirish.

$$-100x+x^{2}=-196$$

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

$$x^{2}-100x=-196$$

-100 ni bo‘lish, x shartining koeffitsienti, 2 ga -50 olish uchun. Keyin, -50 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-100x+\left(-50\right)^{2}=-196+\left(-50\right)^{2}$$

-50 kvadratini chiqarish.

$$x^{2}-100x+2500=-196+2500$$

-196 ni 2500 ga qo'shish.

$$x^{2}-100x+2500=2304$$

x^{2}-100x+2500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-50\right)^{2}=2304$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-50\right)^{2}}=\sqrt{2304}$$

Qisqartirish.

$$x-50=48 x-50=-48$$

50 ni tenglamaning ikkala tarafiga qo'shish.

$$x=98 x=2$$