29500x^2-7644x=40248 eching

$$29500 x ^ { 2 } - 7644 x = 40248$$

x uchun yechish

$$x = \frac{9 \sqrt{3709641} + 1911}{14750} \approx 1,304771899$$

$$x=\frac{1911-9\sqrt{3709641}}{14750}\approx -1,045653255$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$29500x^{2}-7644x=40248$$

Tenglamaning ikkala tarafidan 40248 ni ayirish.

$$29500x^{2}-7644x-40248=40248-40248$$

O‘zidan 40248 ayirilsa 0 qoladi.

$$29500x^{2}-7644x-40248=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 29500 ni a, -7644 ni b va -40248 ni c bilan almashtiring.

$$x=\frac{-\left(-7644\right)±\sqrt{\left(-7644\right)^{2}-4\times 29500\left(-40248\right)}}{2\times 29500}$$

-7644 kvadratini chiqarish.

$$x=\frac{-\left(-7644\right)±\sqrt{58430736-4\times 29500\left(-40248\right)}}{2\times 29500}$$

-4 ni 29500 marotabaga ko'paytirish.

$$x=\frac{-\left(-7644\right)±\sqrt{58430736-118000\left(-40248\right)}}{2\times 29500}$$

-118000 ni -40248 marotabaga ko'paytirish.

$$x=\frac{-\left(-7644\right)±\sqrt{58430736+4749264000}}{2\times 29500}$$

58430736 ni 4749264000 ga qo'shish.

$$x=\frac{-\left(-7644\right)±\sqrt{4807694736}}{2\times 29500}$$

4807694736 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-7644\right)±36\sqrt{3709641}}{2\times 29500}$$

-7644 ning teskarisi 7644 ga teng.

$$x=\frac{7644±36\sqrt{3709641}}{2\times 29500}$$

2 ni 29500 marotabaga ko'paytirish.

$$x=\frac{7644±36\sqrt{3709641}}{59000}$$

x=\frac{7644±36\sqrt{3709641}}{59000} tenglamasini yeching, bunda ± musbat. 7644 ni 36\sqrt{3709641} ga qo'shish.

$$x=\frac{36\sqrt{3709641}+7644}{59000}$$

7644+36\sqrt{3709641} ni 59000 ga bo'lish.

$$x=\frac{9\sqrt{3709641}+1911}{14750}$$

x=\frac{7644±36\sqrt{3709641}}{59000} tenglamasini yeching, bunda ± manfiy. 7644 dan 36\sqrt{3709641} ni ayirish.

$$x=\frac{7644-36\sqrt{3709641}}{59000}$$

7644-36\sqrt{3709641} ni 59000 ga bo'lish.

$$x=\frac{1911-9\sqrt{3709641}}{14750}$$

Tenglama yechildi.

$$x=\frac{9\sqrt{3709641}+1911}{14750} x=\frac{1911-9\sqrt{3709641}}{14750}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$29500x^{2}-7644x=40248$$

Ikki tarafini 29500 ga bo‘ling.

$$\frac{29500x^{2}-7644x}{29500}=\frac{40248}{29500}$$

29500 ga bo'lish 29500 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{7644}{29500}\right)x=\frac{40248}{29500}$$

\frac{-7644}{29500} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1911}{7375}x=\frac{40248}{29500}$$

\frac{40248}{29500} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1911}{7375}x=\frac{10062}{7375}$$

-\frac{1911}{7375} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1911}{14750} olish uchun. Keyin, -\frac{1911}{14750} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1911}{7375}x+\left(-\frac{1911}{14750}\right)^{2}=\frac{10062}{7375}+\left(-\frac{1911}{14750}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1911}{14750} kvadratini chiqarish.

$$x^{2}-\frac{1911}{7375}x+\frac{3651921}{217562500}=\frac{10062}{7375}+\frac{3651921}{217562500}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{10062}{7375} ni \frac{3651921}{217562500} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1911}{7375}x+\frac{3651921}{217562500}=\frac{300480921}{217562500}$$

x^{2}-\frac{1911}{7375}x+\frac{3651921}{217562500} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1911}{14750}\right)^{2}=\frac{300480921}{217562500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1911}{14750}\right)^{2}}=\sqrt{\frac{300480921}{217562500}}$$

Qisqartirish.

$$x-\frac{1911}{14750}=\frac{9\sqrt{3709641}}{14750} x-\frac{1911}{14750}=-\frac{9\sqrt{3709641}}{14750}$$

\frac{1911}{14750} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{9\sqrt{3709641}+1911}{14750} x=\frac{1911-9\sqrt{3709641}}{14750}$$