x^2-406x+163^2=0 eching

$${ x }^{ 2 } -406x+ { 163 }^{ 2 } =0$$

x uchun yechish

$$x=4\sqrt{915}+203\approx 323,995867698$$

$$x=203-4\sqrt{915}\approx 82,004132302$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 163 ga hisoblang va 26569 ni qiymatni oling.

$$x^{2}-406x+26569=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -406 ni b va 26569 ni c bilan almashtiring.

$$x=\frac{-\left(-406\right)±\sqrt{\left(-406\right)^{2}-4\times 26569}}{2}$$

-406 kvadratini chiqarish.

$$x=\frac{-\left(-406\right)±\sqrt{164836-4\times 26569}}{2}$$

-4 ni 26569 marotabaga ko'paytirish.

$$x=\frac{-\left(-406\right)±\sqrt{164836-106276}}{2}$$

164836 ni -106276 ga qo'shish.

$$x=\frac{-\left(-406\right)±\sqrt{58560}}{2}$$

58560 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-406\right)±8\sqrt{915}}{2}$$

-406 ning teskarisi 406 ga teng.

$$x=\frac{406±8\sqrt{915}}{2}$$

x=\frac{406±8\sqrt{915}}{2} tenglamasini yeching, bunda ± musbat. 406 ni 8\sqrt{915} ga qo'shish.

$$x=\frac{8\sqrt{915}+406}{2}$$

406+8\sqrt{915} ni 2 ga bo'lish.

$$x=4\sqrt{915}+203$$

x=\frac{406±8\sqrt{915}}{2} tenglamasini yeching, bunda ± manfiy. 406 dan 8\sqrt{915} ni ayirish.

$$x=\frac{406-8\sqrt{915}}{2}$$

406-8\sqrt{915} ni 2 ga bo'lish.

$$x=203-4\sqrt{915}$$

Tenglama yechildi.

$$x=4\sqrt{915}+203 x=203-4\sqrt{915}$$

Kvadratni yakunlash bo'yicha qadamlar

2 daraja ko‘rsatkichini 163 ga hisoblang va 26569 ni qiymatni oling.

$$x^{2}-406x+26569=0$$

Ikkala tarafdan 26569 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-406x=-26569$$

-406 ni bo‘lish, x shartining koeffitsienti, 2 ga -203 olish uchun. Keyin, -203 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-406x+\left(-203\right)^{2}=-26569+\left(-203\right)^{2}$$

-203 kvadratini chiqarish.

$$x^{2}-406x+41209=-26569+41209$$

-26569 ni 41209 ga qo'shish.

$$x^{2}-406x+41209=14640$$

x^{2}-406x+41209 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-203\right)^{2}=14640$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-203\right)^{2}}=\sqrt{14640}$$

Qisqartirish.

$$x-203=4\sqrt{915} x-203=-4\sqrt{915}$$

203 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4\sqrt{915}+203 x=203-4\sqrt{915}$$