4x+55x-9^2=99999x^2 eching

$$4x+55x- { 9 }^{ 2 } =99999 { x }^{ 2 }$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{32396195}i+59}{199998}\approx 0,000295003-0,028459112i$$

$$x=\frac{59+\sqrt{32396195}i}{199998}\approx 0,000295003+0,028459112i$$

Kvadrat tenglamalaridan foydalanish qoidalari

59x ni olish uchun 4x va 55x ni birlashtirish.

$$59x-9^{2}=99999x^{2}$$

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$59x-81=99999x^{2}$$

Ikkala tarafdan 99999x^{2} ni ayirish.

$$59x-81-99999x^{2}=0$$

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.

$$-99999x^{2}+59x-81=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -99999 ni a, 59 ni b va -81 ni c bilan almashtiring.

$$x=\frac{-59±\sqrt{59^{2}-4\left(-99999\right)\left(-81\right)}}{2\left(-99999\right)}$$

59 kvadratini chiqarish.

$$x=\frac{-59±\sqrt{3481-4\left(-99999\right)\left(-81\right)}}{2\left(-99999\right)}$$

-4 ni -99999 marotabaga ko'paytirish.

$$x=\frac{-59±\sqrt{3481+399996\left(-81\right)}}{2\left(-99999\right)}$$

399996 ni -81 marotabaga ko'paytirish.

$$x=\frac{-59±\sqrt{3481-32399676}}{2\left(-99999\right)}$$

3481 ni -32399676 ga qo'shish.

$$x=\frac{-59±\sqrt{-32396195}}{2\left(-99999\right)}$$

-32396195 ning kvadrat ildizini chiqarish.

$$x=\frac{-59±\sqrt{32396195}i}{2\left(-99999\right)}$$

2 ni -99999 marotabaga ko'paytirish.

$$x=\frac{-59±\sqrt{32396195}i}{-199998}$$

x=\frac{-59±\sqrt{32396195}i}{-199998} tenglamasini yeching, bunda ± musbat. -59 ni i\sqrt{32396195} ga qo'shish.

$$x=\frac{-59+\sqrt{32396195}i}{-199998}$$

-59+i\sqrt{32396195} ni -199998 ga bo'lish.

$$x=\frac{-\sqrt{32396195}i+59}{199998}$$

x=\frac{-59±\sqrt{32396195}i}{-199998} tenglamasini yeching, bunda ± manfiy. -59 dan i\sqrt{32396195} ni ayirish.

$$x=\frac{-\sqrt{32396195}i-59}{-199998}$$

-59-i\sqrt{32396195} ni -199998 ga bo'lish.

$$x=\frac{59+\sqrt{32396195}i}{199998}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{32396195}i+59}{199998} x=\frac{59+\sqrt{32396195}i}{199998}$$

Kvadratni yakunlash bo'yicha qadamlar

59x ni olish uchun 4x va 55x ni birlashtirish.

$$59x-9^{2}=99999x^{2}$$

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$59x-81=99999x^{2}$$

Ikkala tarafdan 99999x^{2} ni ayirish.

$$59x-81-99999x^{2}=0$$

81 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$59x-99999x^{2}=81$$

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

$$-99999x^{2}+59x=81$$

Ikki tarafini -99999 ga bo‘ling.

$$\frac{-99999x^{2}+59x}{-99999}=\frac{81}{-99999}$$

-99999 ga bo'lish -99999 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{59}{-99999}x=\frac{81}{-99999}$$

59 ni -99999 ga bo'lish.

$$x^{2}-\frac{59}{99999}x=\frac{81}{-99999}$$

\frac{81}{-99999} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{59}{99999}x=-\frac{9}{11111}$$

-\frac{59}{99999} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{59}{199998} olish uchun. Keyin, -\frac{59}{199998} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{59}{99999}x+\left(-\frac{59}{199998}\right)^{2}=-\frac{9}{11111}+\left(-\frac{59}{199998}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{59}{199998} kvadratini chiqarish.

$$x^{2}-\frac{59}{99999}x+\frac{3481}{39999200004}=-\frac{9}{11111}+\frac{3481}{39999200004}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{9}{11111} ni \frac{3481}{39999200004} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{59}{99999}x+\frac{3481}{39999200004}=-\frac{32396195}{39999200004}$$

x^{2}-\frac{59}{99999}x+\frac{3481}{39999200004} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{59}{199998}\right)^{2}=-\frac{32396195}{39999200004}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{59}{199998}\right)^{2}}=\sqrt{-\frac{32396195}{39999200004}}$$

Qisqartirish.

$$x-\frac{59}{199998}=\frac{\sqrt{32396195}i}{199998} x-\frac{59}{199998}=-\frac{\sqrt{32396195}i}{199998}$$

\frac{59}{199998} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{59+\sqrt{32396195}i}{199998} x=\frac{-\sqrt{32396195}i+59}{199998}$$