x+120*66/1266-x=76 eching

$$x + \frac { 120 \times 66 } { 1266 - x } = 76$$

x uchun yechish

$$x=\sqrt{361945}+671\approx 1272,618649977$$

$$x=671-\sqrt{361945}\approx 69,381350023$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 1266 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+1266 ga ko'paytirish.

$$\left(-x+1266\right)x+120\times 66=76\left(-x+1266\right)$$

-x+1266 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-x^{2}+1266x+120\times 66=76\left(-x+1266\right)$$

7920 hosil qilish uchun 120 va 66 ni ko'paytirish.

$$-x^{2}+1266x+7920=76\left(-x+1266\right)$$

76 ga -x+1266 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-x^{2}+1266x+7920=-76x+96216$$

76x ni ikki tarafga qo’shing.

$$-x^{2}+1266x+7920+76x=96216$$

1342x ni olish uchun 1266x va 76x ni birlashtirish.

$$-x^{2}+1342x+7920=96216$$

Ikkala tarafdan 96216 ni ayirish.

$$-x^{2}+1342x+7920-96216=0$$

-88296 olish uchun 7920 dan 96216 ni ayirish.

$$-x^{2}+1342x-88296=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 1342 ni b va -88296 ni c bilan almashtiring.

$$x=\frac{-1342±\sqrt{1342^{2}-4\left(-1\right)\left(-88296\right)}}{2\left(-1\right)}$$

1342 kvadratini chiqarish.

$$x=\frac{-1342±\sqrt{1800964-4\left(-1\right)\left(-88296\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1342±\sqrt{1800964+4\left(-88296\right)}}{2\left(-1\right)}$$

4 ni -88296 marotabaga ko'paytirish.

$$x=\frac{-1342±\sqrt{1800964-353184}}{2\left(-1\right)}$$

1800964 ni -353184 ga qo'shish.

$$x=\frac{-1342±\sqrt{1447780}}{2\left(-1\right)}$$

1447780 ning kvadrat ildizini chiqarish.

$$x=\frac{-1342±2\sqrt{361945}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1342±2\sqrt{361945}}{-2}$$

x=\frac{-1342±2\sqrt{361945}}{-2} tenglamasini yeching, bunda ± musbat. -1342 ni 2\sqrt{361945} ga qo'shish.

$$x=\frac{2\sqrt{361945}-1342}{-2}$$

-1342+2\sqrt{361945} ni -2 ga bo'lish.

$$x=671-\sqrt{361945}$$

x=\frac{-1342±2\sqrt{361945}}{-2} tenglamasini yeching, bunda ± manfiy. -1342 dan 2\sqrt{361945} ni ayirish.

$$x=\frac{-2\sqrt{361945}-1342}{-2}$$

-1342-2\sqrt{361945} ni -2 ga bo'lish.

$$x=\sqrt{361945}+671$$

Tenglama yechildi.

$$x=671-\sqrt{361945} x=\sqrt{361945}+671$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 1266 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+1266 ga ko'paytirish.

$$\left(-x+1266\right)x+120\times 66=76\left(-x+1266\right)$$

-x+1266 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-x^{2}+1266x+120\times 66=76\left(-x+1266\right)$$

7920 hosil qilish uchun 120 va 66 ni ko'paytirish.

$$-x^{2}+1266x+7920=76\left(-x+1266\right)$$

76 ga -x+1266 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-x^{2}+1266x+7920=-76x+96216$$

76x ni ikki tarafga qo’shing.

$$-x^{2}+1266x+7920+76x=96216$$

1342x ni olish uchun 1266x va 76x ni birlashtirish.

$$-x^{2}+1342x+7920=96216$$

Ikkala tarafdan 7920 ni ayirish.

$$-x^{2}+1342x=96216-7920$$

88296 olish uchun 96216 dan 7920 ni ayirish.

$$-x^{2}+1342x=88296$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+1342x}{-1}=\frac{88296}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1342}{-1}x=\frac{88296}{-1}$$

1342 ni -1 ga bo'lish.

$$x^{2}-1342x=\frac{88296}{-1}$$

88296 ni -1 ga bo'lish.

$$x^{2}-1342x=-88296$$

-1342 ni bo‘lish, x shartining koeffitsienti, 2 ga -671 olish uchun. Keyin, -671 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-1342x+\left(-671\right)^{2}=-88296+\left(-671\right)^{2}$$

-671 kvadratini chiqarish.

$$x^{2}-1342x+450241=-88296+450241$$

-88296 ni 450241 ga qo'shish.

$$x^{2}-1342x+450241=361945$$

x^{2}-1342x+450241 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-671\right)^{2}=361945$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-671\right)^{2}}=\sqrt{361945}$$

Qisqartirish.

$$x-671=\sqrt{361945} x-671=-\sqrt{361945}$$

671 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{361945}+671 x=671-\sqrt{361945}$$