130213=122*(1300+x)*x eching

$$130213=122 \times (1300+x) \times x$$

x uchun yechish

$$x=\frac{\sqrt{6304375986}}{122}-650\approx 0,820497274$$

$$x=-\frac{\sqrt{6304375986}}{122}-650\approx -1300,820497274$$

Kvadrat tenglamalaridan foydalanish qoidalari

122 ga 1300+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$130213=\left(158600+122x\right)x$$

158600+122x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$130213=158600x+122x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$158600x+122x^{2}=130213$$

Ikkala tarafdan 130213 ni ayirish.

$$158600x+122x^{2}-130213=0$$

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.

$$122x^{2}+158600x-130213=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 122 ni a, 158600 ni b va -130213 ni c bilan almashtiring.

$$x=\frac{-158600±\sqrt{158600^{2}-4\times 122\left(-130213\right)}}{2\times 122}$$

158600 kvadratini chiqarish.

$$x=\frac{-158600±\sqrt{25153960000-4\times 122\left(-130213\right)}}{2\times 122}$$

-4 ni 122 marotabaga ko'paytirish.

$$x=\frac{-158600±\sqrt{25153960000-488\left(-130213\right)}}{2\times 122}$$

-488 ni -130213 marotabaga ko'paytirish.

$$x=\frac{-158600±\sqrt{25153960000+63543944}}{2\times 122}$$

25153960000 ni 63543944 ga qo'shish.

$$x=\frac{-158600±\sqrt{25217503944}}{2\times 122}$$

25217503944 ning kvadrat ildizini chiqarish.

$$x=\frac{-158600±2\sqrt{6304375986}}{2\times 122}$$

2 ni 122 marotabaga ko'paytirish.

$$x=\frac{-158600±2\sqrt{6304375986}}{244}$$

x=\frac{-158600±2\sqrt{6304375986}}{244} tenglamasini yeching, bunda ± musbat. -158600 ni 2\sqrt{6304375986} ga qo'shish.

$$x=\frac{2\sqrt{6304375986}-158600}{244}$$

-158600+2\sqrt{6304375986} ni 244 ga bo'lish.

$$x=\frac{\sqrt{6304375986}}{122}-650$$

x=\frac{-158600±2\sqrt{6304375986}}{244} tenglamasini yeching, bunda ± manfiy. -158600 dan 2\sqrt{6304375986} ni ayirish.

$$x=\frac{-2\sqrt{6304375986}-158600}{244}$$

-158600-2\sqrt{6304375986} ni 244 ga bo'lish.

$$x=-\frac{\sqrt{6304375986}}{122}-650$$

Tenglama yechildi.

$$x=\frac{\sqrt{6304375986}}{122}-650 x=-\frac{\sqrt{6304375986}}{122}-650$$

Kvadratni yakunlash bo'yicha qadamlar

122 ga 1300+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$130213=\left(158600+122x\right)x$$

158600+122x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$130213=158600x+122x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$158600x+122x^{2}=130213$$

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

$$122x^{2}+158600x=130213$$

Ikki tarafini 122 ga bo‘ling.

$$\frac{122x^{2}+158600x}{122}=\frac{130213}{122}$$

122 ga bo'lish 122 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{158600}{122}x=\frac{130213}{122}$$

158600 ni 122 ga bo'lish.

$$x^{2}+1300x=\frac{130213}{122}$$

1300 ni bo‘lish, x shartining koeffitsienti, 2 ga 650 olish uchun. Keyin, 650 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+1300x+650^{2}=\frac{130213}{122}+650^{2}$$

650 kvadratini chiqarish.

$$x^{2}+1300x+422500=\frac{130213}{122}+422500$$

\frac{130213}{122} ni 422500 ga qo'shish.

$$x^{2}+1300x+422500=\frac{51675213}{122}$$

x^{2}+1300x+422500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+650\right)^{2}=\frac{51675213}{122}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+650\right)^{2}}=\sqrt{\frac{51675213}{122}}$$

Qisqartirish.

$$x+650=\frac{\sqrt{6304375986}}{122} x+650=-\frac{\sqrt{6304375986}}{122}$$

Tenglamaning ikkala tarafidan 650 ni ayirish.

$$x=\frac{\sqrt{6304375986}}{122}-650 x=-\frac{\sqrt{6304375986}}{122}-650$$