(2x-40)(3x-50)*(30+100)+2000*1000=64000 eching

$$( 2 x - 40 ) ( 3 x - 50 ) \times ( 30 + 100 ) + 2000 \times 1000 = 64000$$

x uchun yechish (complex solution)

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3}\approx 18,333333333+49,792303665i$$

$$x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}\approx 18,333333333-49,792303665i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 1000=64000$$

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

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 1000=64000$$

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

$$780x^{2}-28600x+260000+2000\times 1000=64000$$

2000000 hosil qilish uchun 2000 va 1000 ni ko'paytirish.

$$780x^{2}-28600x+260000+2000000=64000$$

2260000 olish uchun 260000 va 2000000'ni qo'shing.

$$780x^{2}-28600x+2260000=64000$$

Ikkala tarafdan 64000 ni ayirish.

$$780x^{2}-28600x+2260000-64000=0$$

2196000 olish uchun 2260000 dan 64000 ni ayirish.

$$780x^{2}-28600x+2196000=0$$

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 2196000 ni c bilan almashtiring.

$$x=\frac{-\left(-28600\right)±\sqrt{\left(-28600\right)^{2}-4\times 780\times 2196000}}{2\times 780}$$

-28600 kvadratini chiqarish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-4\times 780\times 2196000}}{2\times 780}$$

-4 ni 780 marotabaga ko'paytirish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-3120\times 2196000}}{2\times 780}$$

-3120 ni 2196000 marotabaga ko'paytirish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-6851520000}}{2\times 780}$$

817960000 ni -6851520000 ga qo'shish.

$$x=\frac{-\left(-28600\right)±\sqrt{-6033560000}}{2\times 780}$$

-6033560000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-28600\right)±200\sqrt{150839}i}{2\times 780}$$

-28600 ning teskarisi 28600 ga teng.

$$x=\frac{28600±200\sqrt{150839}i}{2\times 780}$$

2 ni 780 marotabaga ko'paytirish.

$$x=\frac{28600±200\sqrt{150839}i}{1560}$$

x=\frac{28600±200\sqrt{150839}i}{1560} tenglamasini yeching, bunda ± musbat. 28600 ni 200i\sqrt{150839} ga qo'shish.

$$x=\frac{28600+200\sqrt{150839}i}{1560}$$

28600+200i\sqrt{150839} ni 1560 ga bo'lish.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

x=\frac{28600±200\sqrt{150839}i}{1560} tenglamasini yeching, bunda ± manfiy. 28600 dan 200i\sqrt{150839} ni ayirish.

$$x=\frac{-200\sqrt{150839}i+28600}{1560}$$

28600-200i\sqrt{150839} ni 1560 ga bo'lish.

$$x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3} x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 1000=64000$$

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

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 1000=64000$$

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

$$780x^{2}-28600x+260000+2000\times 1000=64000$$

2000000 hosil qilish uchun 2000 va 1000 ni ko'paytirish.

$$780x^{2}-28600x+260000+2000000=64000$$

2260000 olish uchun 260000 va 2000000'ni qo'shing.

$$780x^{2}-28600x+2260000=64000$$

Ikkala tarafdan 2260000 ni ayirish.

$$780x^{2}-28600x=64000-2260000$$

-2196000 olish uchun 64000 dan 2260000 ni ayirish.

$$780x^{2}-28600x=-2196000$$

Ikki tarafini 780 ga bo‘ling.

$$\frac{780x^{2}-28600x}{780}=-\frac{2196000}{780}$$

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

$$x^{2}+\left(-\frac{28600}{780}\right)x=-\frac{2196000}{780}$$

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

$$x^{2}-\frac{110}{3}x=-\frac{2196000}{780}$$

\frac{-2196000}{780} ulushini 60 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{110}{3}x=-\frac{36600}{13}$$

-\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.

$$x^{2}-\frac{110}{3}x+\left(-\frac{55}{3}\right)^{2}=-\frac{36600}{13}+\left(-\frac{55}{3}\right)^{2}$$

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

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=-\frac{36600}{13}+\frac{3025}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{36600}{13} ni \frac{3025}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=-\frac{290075}{117}$$

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.

$$\left(x-\frac{55}{3}\right)^{2}=-\frac{290075}{117}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{55}{3}\right)^{2}}=\sqrt{-\frac{290075}{117}}$$

Qisqartirish.

$$x-\frac{55}{3}=\frac{5\sqrt{150839}i}{39} x-\frac{55}{3}=-\frac{5\sqrt{150839}i}{39}$$

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

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3} x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$