(-01-01)^2+(200-y)-(-115+4)^2=18225 eching

$$( - 01 - 01 ) ^ { 2 } + \{ ( 200 - y ) - ( - 115 + 4 ) \} ^ { 2 } = 18225$$

y uchun yechish

$$y=176$$

$$y=446$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 1 ni ko'paytirish.

$$\left(0-0\times 1\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

0 hosil qilish uchun 0 va 1 ni ko'paytirish.

$$\left(0-0\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

O‘zidan 0 ayirilsa 0 qoladi.

$$0^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$0+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

-111 olish uchun -115 va 4'ni qo'shing.

$$0+\left(200-y-\left(-111\right)\right)^{2}=18225$$

-111 ning teskarisi 111 ga teng.

$$0+\left(200-y+111\right)^{2}=18225$$

200-y+111 kvadratini chiqarish.

$$0+y^{2}-622y+96721=18225$$

96721 olish uchun 0 va 96721'ni qo'shing.

$$96721+y^{2}-622y=18225$$

Ikkala tarafdan 18225 ni ayirish.

$$96721+y^{2}-622y-18225=0$$

78496 olish uchun 96721 dan 18225 ni ayirish.

$$78496+y^{2}-622y=0$$

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.

$$y^{2}-622y+78496=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -622 ni b va 78496 ni c bilan almashtiring.

$$y=\frac{-\left(-622\right)±\sqrt{\left(-622\right)^{2}-4\times 78496}}{2}$$

-622 kvadratini chiqarish.

$$y=\frac{-\left(-622\right)±\sqrt{386884-4\times 78496}}{2}$$

-4 ni 78496 marotabaga ko'paytirish.

$$y=\frac{-\left(-622\right)±\sqrt{386884-313984}}{2}$$

386884 ni -313984 ga qo'shish.

$$y=\frac{-\left(-622\right)±\sqrt{72900}}{2}$$

72900 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-622\right)±270}{2}$$

-622 ning teskarisi 622 ga teng.

$$y=\frac{622±270}{2}$$

y=\frac{622±270}{2} tenglamasini yeching, bunda ± musbat. 622 ni 270 ga qo'shish.

$$y=\frac{892}{2}$$

892 ni 2 ga bo'lish.

$$y=446$$

y=\frac{622±270}{2} tenglamasini yeching, bunda ± manfiy. 622 dan 270 ni ayirish.

$$y=\frac{352}{2}$$

352 ni 2 ga bo'lish.

$$y=176$$

Tenglama yechildi.

$$y=446 y=176$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 1 ni ko'paytirish.

$$\left(0-0\times 1\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

0 hosil qilish uchun 0 va 1 ni ko'paytirish.

$$\left(0-0\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

O‘zidan 0 ayirilsa 0 qoladi.

$$0^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

2 daraja ko‘rsatkichini 0 ga hisoblang va 0 ni qiymatni oling.

$$0+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

-111 olish uchun -115 va 4'ni qo'shing.

$$0+\left(200-y-\left(-111\right)\right)^{2}=18225$$

-111 ning teskarisi 111 ga teng.

$$0+\left(200-y+111\right)^{2}=18225$$

200-y+111 kvadratini chiqarish.

$$0+y^{2}-622y+96721=18225$$

96721 olish uchun 0 va 96721'ni qo'shing.

$$96721+y^{2}-622y=18225$$

Ikkala tarafdan 96721 ni ayirish.

$$y^{2}-622y=18225-96721$$

-78496 olish uchun 18225 dan 96721 ni ayirish.

$$y^{2}-622y=-78496$$

-622 ni bo‘lish, x shartining koeffitsienti, 2 ga -311 olish uchun. Keyin, -311 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-622y+\left(-311\right)^{2}=-78496+\left(-311\right)^{2}$$

-311 kvadratini chiqarish.

$$y^{2}-622y+96721=-78496+96721$$

-78496 ni 96721 ga qo'shish.

$$y^{2}-622y+96721=18225$$

y^{2}-622y+96721 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-311\right)^{2}=18225$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-311\right)^{2}}=\sqrt{18225}$$

Qisqartirish.

$$y-311=135 y-311=-135$$

311 ni tenglamaning ikkala tarafiga qo'shish.

$$y=446 y=176$$