(x(125x+15)-50*40)*30+x(125x+15)*100=6420000 eching

$$(x(125x+15)-50 \times 40) \times 30+x(125x+15) \times 100=6420000$$

x uchun yechish

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50}\approx 19,909297203$$

$$x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}\approx -20,029297203$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga 125x+15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(125x^{2}+15x-50\times 40\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

2000 hosil qilish uchun 50 va 40 ni ko'paytirish.

$$\left(125x^{2}+15x-2000\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

125x^{2}+15x-2000 ga 30 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3750x^{2}+450x-60000+x\left(125x+15\right)\times 100=6420000$$

x ga 125x+15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3750x^{2}+450x-60000+\left(125x^{2}+15x\right)\times 100=6420000$$

125x^{2}+15x ga 100 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3750x^{2}+450x-60000+12500x^{2}+1500x=6420000$$

16250x^{2} ni olish uchun 3750x^{2} va 12500x^{2} ni birlashtirish.

$$16250x^{2}+450x-60000+1500x=6420000$$

1950x ni olish uchun 450x va 1500x ni birlashtirish.

$$16250x^{2}+1950x-60000=6420000$$

Ikkala tarafdan 6420000 ni ayirish.

$$16250x^{2}+1950x-60000-6420000=0$$

-6480000 olish uchun -60000 dan 6420000 ni ayirish.

$$16250x^{2}+1950x-6480000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 16250 ni a, 1950 ni b va -6480000 ni c bilan almashtiring.

$$x=\frac{-1950±\sqrt{1950^{2}-4\times 16250\left(-6480000\right)}}{2\times 16250}$$

1950 kvadratini chiqarish.

$$x=\frac{-1950±\sqrt{3802500-4\times 16250\left(-6480000\right)}}{2\times 16250}$$

-4 ni 16250 marotabaga ko'paytirish.

$$x=\frac{-1950±\sqrt{3802500-65000\left(-6480000\right)}}{2\times 16250}$$

-65000 ni -6480000 marotabaga ko'paytirish.

$$x=\frac{-1950±\sqrt{3802500+421200000000}}{2\times 16250}$$

3802500 ni 421200000000 ga qo'shish.

$$x=\frac{-1950±\sqrt{421203802500}}{2\times 16250}$$

421203802500 ning kvadrat ildizini chiqarish.

$$x=\frac{-1950±150\sqrt{18720169}}{2\times 16250}$$

2 ni 16250 marotabaga ko'paytirish.

$$x=\frac{-1950±150\sqrt{18720169}}{32500}$$

x=\frac{-1950±150\sqrt{18720169}}{32500} tenglamasini yeching, bunda ± musbat. -1950 ni 150\sqrt{18720169} ga qo'shish.

$$x=\frac{150\sqrt{18720169}-1950}{32500}$$

-1950+150\sqrt{18720169} ni 32500 ga bo'lish.

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$

x=\frac{-1950±150\sqrt{18720169}}{32500} tenglamasini yeching, bunda ± manfiy. -1950 dan 150\sqrt{18720169} ni ayirish.

$$x=\frac{-150\sqrt{18720169}-1950}{32500}$$

-1950-150\sqrt{18720169} ni 32500 ga bo'lish.

$$x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50} x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$

Kvadratni yakunlash bo'yicha qadamlar

x ga 125x+15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(125x^{2}+15x-50\times 40\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

2000 hosil qilish uchun 50 va 40 ni ko'paytirish.

$$\left(125x^{2}+15x-2000\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

125x^{2}+15x-2000 ga 30 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3750x^{2}+450x-60000+x\left(125x+15\right)\times 100=6420000$$

x ga 125x+15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3750x^{2}+450x-60000+\left(125x^{2}+15x\right)\times 100=6420000$$

125x^{2}+15x ga 100 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3750x^{2}+450x-60000+12500x^{2}+1500x=6420000$$

16250x^{2} ni olish uchun 3750x^{2} va 12500x^{2} ni birlashtirish.

$$16250x^{2}+450x-60000+1500x=6420000$$

1950x ni olish uchun 450x va 1500x ni birlashtirish.

$$16250x^{2}+1950x-60000=6420000$$

60000 ni ikki tarafga qo’shing.

$$16250x^{2}+1950x=6420000+60000$$

6480000 olish uchun 6420000 va 60000'ni qo'shing.

$$16250x^{2}+1950x=6480000$$

Ikki tarafini 16250 ga bo‘ling.

$$\frac{16250x^{2}+1950x}{16250}=\frac{6480000}{16250}$$

16250 ga bo'lish 16250 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1950}{16250}x=\frac{6480000}{16250}$$

\frac{1950}{16250} ulushini 650 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{3}{25}x=\frac{6480000}{16250}$$

\frac{6480000}{16250} ulushini 1250 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{3}{25}x=\frac{5184}{13}$$

\frac{3}{25} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{50} olish uchun. Keyin, \frac{3}{50} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{25}x+\left(\frac{3}{50}\right)^{2}=\frac{5184}{13}+\left(\frac{3}{50}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{50} kvadratini chiqarish.

$$x^{2}+\frac{3}{25}x+\frac{9}{2500}=\frac{5184}{13}+\frac{9}{2500}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5184}{13} ni \frac{9}{2500} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{3}{25}x+\frac{9}{2500}=\frac{12960117}{32500}$$

x^{2}+\frac{3}{25}x+\frac{9}{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.

$$\left(x+\frac{3}{50}\right)^{2}=\frac{12960117}{32500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{50}\right)^{2}}=\sqrt{\frac{12960117}{32500}}$$

Qisqartirish.

$$x+\frac{3}{50}=\frac{3\sqrt{18720169}}{650} x+\frac{3}{50}=-\frac{3\sqrt{18720169}}{650}$$

Tenglamaning ikkala tarafidan \frac{3}{50} ni ayirish.

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50} x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$