418392+2*78*98x=65*10^4quadx^2 eching

$$418392 + 2 \times 78 \times 98 x = 65 \times 10 ^ { 4 } \quad x ^ { 2 }$$

x uchun yechish

$$x=\frac{3\sqrt{11177401}+147}{12500}\approx 0,814142887$$

$$x=\frac{147-3\sqrt{11177401}}{12500}\approx -0,790622887$$

Kvadrat tenglamalaridan foydalanish qoidalari

156 hosil qilish uchun 2 va 78 ni ko'paytirish.

$$418392+156\times 98x=65\times 10^{4}x^{2}$$

15288 hosil qilish uchun 156 va 98 ni ko'paytirish.

$$418392+15288x=65\times 10^{4}x^{2}$$

4 daraja ko‘rsatkichini 10 ga hisoblang va 10000 ni qiymatni oling.

$$418392+15288x=65\times 10000x^{2}$$

650000 hosil qilish uchun 65 va 10000 ni ko'paytirish.

$$418392+15288x=650000x^{2}$$

Ikkala tarafdan 650000x^{2} ni ayirish.

$$418392+15288x-650000x^{2}=0$$

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.

$$-650000x^{2}+15288x+418392=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -650000 ni a, 15288 ni b va 418392 ni c bilan almashtiring.

$$x=\frac{-15288±\sqrt{15288^{2}-4\left(-650000\right)\times 418392}}{2\left(-650000\right)}$$

15288 kvadratini chiqarish.

$$x=\frac{-15288±\sqrt{233722944-4\left(-650000\right)\times 418392}}{2\left(-650000\right)}$$

-4 ni -650000 marotabaga ko'paytirish.

$$x=\frac{-15288±\sqrt{233722944+2600000\times 418392}}{2\left(-650000\right)}$$

2600000 ni 418392 marotabaga ko'paytirish.

$$x=\frac{-15288±\sqrt{233722944+1087819200000}}{2\left(-650000\right)}$$

233722944 ni 1087819200000 ga qo'shish.

$$x=\frac{-15288±\sqrt{1088052922944}}{2\left(-650000\right)}$$

1088052922944 ning kvadrat ildizini chiqarish.

$$x=\frac{-15288±312\sqrt{11177401}}{2\left(-650000\right)}$$

2 ni -650000 marotabaga ko'paytirish.

$$x=\frac{-15288±312\sqrt{11177401}}{-1300000}$$

x=\frac{-15288±312\sqrt{11177401}}{-1300000} tenglamasini yeching, bunda ± musbat. -15288 ni 312\sqrt{11177401} ga qo'shish.

$$x=\frac{312\sqrt{11177401}-15288}{-1300000}$$

-15288+312\sqrt{11177401} ni -1300000 ga bo'lish.

$$x=\frac{147-3\sqrt{11177401}}{12500}$$

x=\frac{-15288±312\sqrt{11177401}}{-1300000} tenglamasini yeching, bunda ± manfiy. -15288 dan 312\sqrt{11177401} ni ayirish.

$$x=\frac{-312\sqrt{11177401}-15288}{-1300000}$$

-15288-312\sqrt{11177401} ni -1300000 ga bo'lish.

$$x=\frac{3\sqrt{11177401}+147}{12500}$$

Tenglama yechildi.

$$x=\frac{147-3\sqrt{11177401}}{12500} x=\frac{3\sqrt{11177401}+147}{12500}$$

Kvadratni yakunlash bo'yicha qadamlar

156 hosil qilish uchun 2 va 78 ni ko'paytirish.

$$418392+156\times 98x=65\times 10^{4}x^{2}$$

15288 hosil qilish uchun 156 va 98 ni ko'paytirish.

$$418392+15288x=65\times 10^{4}x^{2}$$

4 daraja ko‘rsatkichini 10 ga hisoblang va 10000 ni qiymatni oling.

$$418392+15288x=65\times 10000x^{2}$$

650000 hosil qilish uchun 65 va 10000 ni ko'paytirish.

$$418392+15288x=650000x^{2}$$

Ikkala tarafdan 650000x^{2} ni ayirish.

$$418392+15288x-650000x^{2}=0$$

Ikkala tarafdan 418392 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$15288x-650000x^{2}=-418392$$

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

$$-650000x^{2}+15288x=-418392$$

Ikki tarafini -650000 ga bo‘ling.

$$\frac{-650000x^{2}+15288x}{-650000}=-\frac{418392}{-650000}$$

-650000 ga bo'lish -650000 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{15288}{-650000}x=-\frac{418392}{-650000}$$

\frac{15288}{-650000} ulushini 104 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{147}{6250}x=-\frac{418392}{-650000}$$

\frac{-418392}{-650000} ulushini 104 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{147}{6250}x=\frac{4023}{6250}$$

-\frac{147}{6250} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{147}{12500} olish uchun. Keyin, -\frac{147}{12500} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{147}{6250}x+\left(-\frac{147}{12500}\right)^{2}=\frac{4023}{6250}+\left(-\frac{147}{12500}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{147}{12500} kvadratini chiqarish.

$$x^{2}-\frac{147}{6250}x+\frac{21609}{156250000}=\frac{4023}{6250}+\frac{21609}{156250000}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{4023}{6250} ni \frac{21609}{156250000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{147}{6250}x+\frac{21609}{156250000}=\frac{100596609}{156250000}$$

x^{2}-\frac{147}{6250}x+\frac{21609}{156250000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{147}{12500}\right)^{2}=\frac{100596609}{156250000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{147}{12500}\right)^{2}}=\sqrt{\frac{100596609}{156250000}}$$

Qisqartirish.

$$x-\frac{147}{12500}=\frac{3\sqrt{11177401}}{12500} x-\frac{147}{12500}=-\frac{3\sqrt{11177401}}{12500}$$

\frac{147}{12500} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{11177401}+147}{12500} x=\frac{147-3\sqrt{11177401}}{12500}$$