(100-x)(1300-5x)=32000 eching

$$(100-x)(1300-5x)=32000$$

x uchun yechish

$$x=80\sqrt{2}+180\approx 293,13708499$$

$$x=180-80\sqrt{2}\approx 66,86291501$$

Kvadrat tenglamalaridan foydalanish qoidalari

100-x ga 1300-5x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$130000-1800x+5x^{2}=32000$$

Ikkala tarafdan 32000 ni ayirish.

$$130000-1800x+5x^{2}-32000=0$$

98000 olish uchun 130000 dan 32000 ni ayirish.

$$98000-1800x+5x^{2}=0$$

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.

$$5x^{2}-1800x+98000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -1800 ni b va 98000 ni c bilan almashtiring.

$$x=\frac{-\left(-1800\right)±\sqrt{\left(-1800\right)^{2}-4\times 5\times 98000}}{2\times 5}$$

-1800 kvadratini chiqarish.

$$x=\frac{-\left(-1800\right)±\sqrt{3240000-4\times 5\times 98000}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-1800\right)±\sqrt{3240000-20\times 98000}}{2\times 5}$$

-20 ni 98000 marotabaga ko'paytirish.

$$x=\frac{-\left(-1800\right)±\sqrt{3240000-1960000}}{2\times 5}$$

3240000 ni -1960000 ga qo'shish.

$$x=\frac{-\left(-1800\right)±\sqrt{1280000}}{2\times 5}$$

1280000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1800\right)±800\sqrt{2}}{2\times 5}$$

-1800 ning teskarisi 1800 ga teng.

$$x=\frac{1800±800\sqrt{2}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{1800±800\sqrt{2}}{10}$$

x=\frac{1800±800\sqrt{2}}{10} tenglamasini yeching, bunda ± musbat. 1800 ni 800\sqrt{2} ga qo'shish.

$$x=\frac{800\sqrt{2}+1800}{10}$$

1800+800\sqrt{2} ni 10 ga bo'lish.

$$x=80\sqrt{2}+180$$

x=\frac{1800±800\sqrt{2}}{10} tenglamasini yeching, bunda ± manfiy. 1800 dan 800\sqrt{2} ni ayirish.

$$x=\frac{1800-800\sqrt{2}}{10}$$

1800-800\sqrt{2} ni 10 ga bo'lish.

$$x=180-80\sqrt{2}$$

Tenglama yechildi.

$$x=80\sqrt{2}+180 x=180-80\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

100-x ga 1300-5x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$130000-1800x+5x^{2}=32000$$

Ikkala tarafdan 130000 ni ayirish.

$$-1800x+5x^{2}=32000-130000$$

-98000 olish uchun 32000 dan 130000 ni ayirish.

$$-1800x+5x^{2}=-98000$$

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

$$5x^{2}-1800x=-98000$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-1800x}{5}=-\frac{98000}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{1800}{5}\right)x=-\frac{98000}{5}$$

-1800 ni 5 ga bo'lish.

$$x^{2}-360x=-\frac{98000}{5}$$

-98000 ni 5 ga bo'lish.

$$x^{2}-360x=-19600$$

-360 ni bo‘lish, x shartining koeffitsienti, 2 ga -180 olish uchun. Keyin, -180 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-360x+\left(-180\right)^{2}=-19600+\left(-180\right)^{2}$$

-180 kvadratini chiqarish.

$$x^{2}-360x+32400=-19600+32400$$

-19600 ni 32400 ga qo'shish.

$$x^{2}-360x+32400=12800$$

x^{2}-360x+32400 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-180\right)^{2}=12800$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-180\right)^{2}}=\sqrt{12800}$$

Qisqartirish.

$$x-180=80\sqrt{2} x-180=-80\sqrt{2}$$

180 ni tenglamaning ikkala tarafiga qo'shish.

$$x=80\sqrt{2}+180 x=180-80\sqrt{2}$$