-500000x^2+45x-9*10^-6=0 eching

$$-500000 { x }^{ 2 } +45x-9 \times { 10 }^{ -6 } = 0$$

x uchun yechish

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0,0000898$$

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0,0000002$$

Kvadrat tenglamalaridan foydalanish qoidalari

-6 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000000} ni qiymatni oling.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

\frac{9}{1000000} hosil qilish uchun 9 va \frac{1}{1000000} ni ko'paytirish.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -500000 ni a, 45 ni b va -\frac{9}{1000000} ni c bilan almashtiring.

$$x=\frac{-45±\sqrt{45^{2}-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

45 kvadratini chiqarish.

$$x=\frac{-45±\sqrt{2025-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

-4 ni -500000 marotabaga ko'paytirish.

$$x=\frac{-45±\sqrt{2025+2000000\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

2000000 ni -\frac{9}{1000000} marotabaga ko'paytirish.

$$x=\frac{-45±\sqrt{2025-18}}{2\left(-500000\right)}$$

2025 ni -18 ga qo'shish.

$$x=\frac{-45±\sqrt{2007}}{2\left(-500000\right)}$$

2007 ning kvadrat ildizini chiqarish.

$$x=\frac{-45±3\sqrt{223}}{2\left(-500000\right)}$$

2 ni -500000 marotabaga ko'paytirish.

$$x=\frac{-45±3\sqrt{223}}{-1000000}$$

x=\frac{-45±3\sqrt{223}}{-1000000} tenglamasini yeching, bunda ± musbat. -45 ni 3\sqrt{223} ga qo'shish.

$$x=\frac{3\sqrt{223}-45}{-1000000}$$

-45+3\sqrt{223} ni -1000000 ga bo'lish.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

x=\frac{-45±3\sqrt{223}}{-1000000} tenglamasini yeching, bunda ± manfiy. -45 dan 3\sqrt{223} ni ayirish.

$$x=\frac{-3\sqrt{223}-45}{-1000000}$$

-45-3\sqrt{223} ni -1000000 ga bo'lish.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Tenglama yechildi.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Kvadratni yakunlash bo'yicha qadamlar

-6 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000000} ni qiymatni oling.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

\frac{9}{1000000} hosil qilish uchun 9 va \frac{1}{1000000} ni ko'paytirish.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

\frac{9}{1000000} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-500000x^{2}+45x=\frac{9}{1000000}$$

Ikki tarafini -500000 ga bo‘ling.

$$\frac{-500000x^{2}+45x}{-500000}=\frac{\frac{9}{1000000}}{-500000}$$

-500000 ga bo'lish -500000 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{45}{-500000}x=\frac{\frac{9}{1000000}}{-500000}$$

\frac{45}{-500000} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{9}{100000}x=\frac{\frac{9}{1000000}}{-500000}$$

\frac{9}{1000000} ni -500000 ga bo'lish.

$$x^{2}-\frac{9}{100000}x=-\frac{9}{500000000000}$$

-\frac{9}{100000} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{200000} olish uchun. Keyin, -\frac{9}{200000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{9}{100000}x+\left(-\frac{9}{200000}\right)^{2}=-\frac{9}{500000000000}+\left(-\frac{9}{200000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{200000} kvadratini chiqarish.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=-\frac{9}{500000000000}+\frac{81}{40000000000}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{9}{500000000000} ni \frac{81}{40000000000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=\frac{2007}{1000000000000}$$

x^{2}-\frac{9}{100000}x+\frac{81}{40000000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{9}{200000}\right)^{2}=\frac{2007}{1000000000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{200000}\right)^{2}}=\sqrt{\frac{2007}{1000000000000}}$$

Qisqartirish.

$$x-\frac{9}{200000}=\frac{3\sqrt{223}}{1000000} x-\frac{9}{200000}=-\frac{3\sqrt{223}}{1000000}$$

\frac{9}{200000} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$