left(2x-40right)left(3x-50right)left(30+100right)+2000*100=642000 eching

$$\left( 2x-40 \right) \left( 3x-50 \right) \left( 30+100 \right) +2000 \cdot 100 = 642000$$

x uchun yechish

$$x = \frac{5 \sqrt{205} + 55}{3} \approx 42,196368439$$

$$x=\frac{55-5\sqrt{205}}{3}\approx -5,529701772$$

Kvadrat tenglamalaridan foydalanish qoidalari

130 olish uchun 30 va 100'ni qo'shing.

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 100=642000$$

2x-40 ga 3x-50 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 100=642000$$

6x^{2}-220x+2000 ga 130 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$780x^{2}-28600x+260000+2000\times 100=642000$$

200000 hosil qilish uchun 2000 va 100 ni ko'paytirish.

$$780x^{2}-28600x+260000+200000=642000$$

460000 olish uchun 260000 va 200000'ni qo'shing.

$$780x^{2}-28600x+460000=642000$$

Ikkala tarafdan 642000 ni ayirish.

$$780x^{2}-28600x+460000-642000=0$$

-182000 olish uchun 460000 dan 642000 ni ayirish.

$$780x^{2}-28600x-182000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 780 ni a, -28600 ni b va -182000 ni c bilan almashtiring.

$$x=\frac{-\left(-28600\right)±\sqrt{\left(-28600\right)^{2}-4\times 780\left(-182000\right)}}{2\times 780}$$

-28600 kvadratini chiqarish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-4\times 780\left(-182000\right)}}{2\times 780}$$

-4 ni 780 marotabaga ko'paytirish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-3120\left(-182000\right)}}{2\times 780}$$

-3120 ni -182000 marotabaga ko'paytirish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000+567840000}}{2\times 780}$$

817960000 ni 567840000 ga qo'shish.

$$x=\frac{-\left(-28600\right)±\sqrt{1385800000}}{2\times 780}$$

1385800000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-28600\right)±2600\sqrt{205}}{2\times 780}$$

-28600 ning teskarisi 28600 ga teng.

$$x=\frac{28600±2600\sqrt{205}}{2\times 780}$$

2 ni 780 marotabaga ko'paytirish.

$$x=\frac{28600±2600\sqrt{205}}{1560}$$

x=\frac{28600±2600\sqrt{205}}{1560} tenglamasini yeching, bunda ± musbat. 28600 ni 2600\sqrt{205} ga qo'shish.

$$x=\frac{2600\sqrt{205}+28600}{1560}$$

28600+2600\sqrt{205} ni 1560 ga bo'lish.

$$x=\frac{5\sqrt{205}+55}{3}$$

x=\frac{28600±2600\sqrt{205}}{1560} tenglamasini yeching, bunda ± manfiy. 28600 dan 2600\sqrt{205} ni ayirish.

$$x=\frac{28600-2600\sqrt{205}}{1560}$$

28600-2600\sqrt{205} ni 1560 ga bo'lish.

$$x=\frac{55-5\sqrt{205}}{3}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{205}+55}{3} x=\frac{55-5\sqrt{205}}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

130 olish uchun 30 va 100'ni qo'shing.

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 100=642000$$

2x-40 ga 3x-50 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 100=642000$$

6x^{2}-220x+2000 ga 130 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$780x^{2}-28600x+260000+2000\times 100=642000$$

200000 hosil qilish uchun 2000 va 100 ni ko'paytirish.

$$780x^{2}-28600x+260000+200000=642000$$

460000 olish uchun 260000 va 200000'ni qo'shing.

$$780x^{2}-28600x+460000=642000$$

Ikkala tarafdan 460000 ni ayirish.

$$780x^{2}-28600x=642000-460000$$

182000 olish uchun 642000 dan 460000 ni ayirish.

$$780x^{2}-28600x=182000$$

Ikki tarafini 780 ga bo‘ling.

$$\frac{780x^{2}-28600x}{780}=\frac{182000}{780}$$

780 ga bo'lish 780 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{28600}{780}\right)x=\frac{182000}{780}$$

\frac{-28600}{780} ulushini 260 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{110}{3}x=\frac{182000}{780}$$

\frac{182000}{780} ulushini 260 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{110}{3}x=\frac{700}{3}$$

-\frac{110}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{55}{3} olish uchun. Keyin, -\frac{55}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{110}{3}x+\left(-\frac{55}{3}\right)^{2}=\frac{700}{3}+\left(-\frac{55}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{55}{3} kvadratini chiqarish.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=\frac{700}{3}+\frac{3025}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{700}{3} ni \frac{3025}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=\frac{5125}{9}$$

x^{2}-\frac{110}{3}x+\frac{3025}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{55}{3}\right)^{2}=\frac{5125}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{55}{3}\right)^{2}}=\sqrt{\frac{5125}{9}}$$

Qisqartirish.

$$x-\frac{55}{3}=\frac{5\sqrt{205}}{3} x-\frac{55}{3}=-\frac{5\sqrt{205}}{3}$$

\frac{55}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5\sqrt{205}+55}{3} x=\frac{55-5\sqrt{205}}{3}$$