-32x^2/130^2+x=264 eching

$$\frac { - 32 x ^ { 2 } } { 130 ^ { 2 } } + x = 264$$

x uchun yechish (complex solution)

$$x=\frac{4225+65\sqrt{4223}i}{16}\approx 264,0625+263,999992602i$$

$$x=\frac{-65\sqrt{4223}i+4225}{16}\approx 264,0625-263,999992602i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 130 ga hisoblang va 16900 ni qiymatni oling.

$$\frac{-32x^{2}}{16900}+x=264$$

-\frac{8}{4225}x^{2} ni olish uchun -32x^{2} ni 16900 ga bo‘ling.

$$-\frac{8}{4225}x^{2}+x=264$$

Ikkala tarafdan 264 ni ayirish.

$$-\frac{8}{4225}x^{2}+x-264=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\frac{8}{4225} ni a, 1 ni b va -264 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-\frac{8}{4225}\right)\left(-264\right)}}{2\left(-\frac{8}{4225}\right)}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-\frac{8}{4225}\right)\left(-264\right)}}{2\left(-\frac{8}{4225}\right)}$$

-4 ni -\frac{8}{4225} marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+\frac{32}{4225}\left(-264\right)}}{2\left(-\frac{8}{4225}\right)}$$

\frac{32}{4225} ni -264 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1-\frac{8448}{4225}}}{2\left(-\frac{8}{4225}\right)}$$

1 ni -\frac{8448}{4225} ga qo'shish.

$$x=\frac{-1±\sqrt{-\frac{4223}{4225}}}{2\left(-\frac{8}{4225}\right)}$$

-\frac{4223}{4225} ning kvadrat ildizini chiqarish.

$$x=\frac{-1±\frac{\sqrt{4223}i}{65}}{2\left(-\frac{8}{4225}\right)}$$

2 ni -\frac{8}{4225} marotabaga ko'paytirish.

$$x=\frac{-1±\frac{\sqrt{4223}i}{65}}{-\frac{16}{4225}}$$

x=\frac{-1±\frac{\sqrt{4223}i}{65}}{-\frac{16}{4225}} tenglamasini yeching, bunda ± musbat. -1 ni \frac{i\sqrt{4223}}{65} ga qo'shish.

$$x=\frac{\frac{\sqrt{4223}i}{65}-1}{-\frac{16}{4225}}$$

-1+\frac{i\sqrt{4223}}{65} ni -\frac{16}{4225} ga bo'lish -1+\frac{i\sqrt{4223}}{65} ga k'paytirish -\frac{16}{4225} ga qaytarish.

$$x=\frac{-65\sqrt{4223}i+4225}{16}$$

x=\frac{-1±\frac{\sqrt{4223}i}{65}}{-\frac{16}{4225}} tenglamasini yeching, bunda ± manfiy. -1 dan \frac{i\sqrt{4223}}{65} ni ayirish.

$$x=\frac{-\frac{\sqrt{4223}i}{65}-1}{-\frac{16}{4225}}$$

-1-\frac{i\sqrt{4223}}{65} ni -\frac{16}{4225} ga bo'lish -1-\frac{i\sqrt{4223}}{65} ga k'paytirish -\frac{16}{4225} ga qaytarish.

$$x=\frac{4225+65\sqrt{4223}i}{16}$$

Tenglama yechildi.

$$x=\frac{-65\sqrt{4223}i+4225}{16} x=\frac{4225+65\sqrt{4223}i}{16}$$

Kvadratni yakunlash bo'yicha qadamlar

2 daraja ko‘rsatkichini 130 ga hisoblang va 16900 ni qiymatni oling.

$$\frac{-32x^{2}}{16900}+x=264$$

-\frac{8}{4225}x^{2} ni olish uchun -32x^{2} ni 16900 ga bo‘ling.

$$-\frac{8}{4225}x^{2}+x=264$$

Tenglamaning ikki tarafini -\frac{8}{4225} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{-\frac{8}{4225}x^{2}+x}{-\frac{8}{4225}}=\frac{264}{-\frac{8}{4225}}$$

-\frac{8}{4225} ga bo'lish -\frac{8}{4225} ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1}{-\frac{8}{4225}}x=\frac{264}{-\frac{8}{4225}}$$

1 ni -\frac{8}{4225} ga bo'lish 1 ga k'paytirish -\frac{8}{4225} ga qaytarish.

$$x^{2}-\frac{4225}{8}x=\frac{264}{-\frac{8}{4225}}$$

264 ni -\frac{8}{4225} ga bo'lish 264 ga k'paytirish -\frac{8}{4225} ga qaytarish.

$$x^{2}-\frac{4225}{8}x=-139425$$

-\frac{4225}{8} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{4225}{16} olish uchun. Keyin, -\frac{4225}{16} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{4225}{8}x+\left(-\frac{4225}{16}\right)^{2}=-139425+\left(-\frac{4225}{16}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{4225}{16} kvadratini chiqarish.

$$x^{2}-\frac{4225}{8}x+\frac{17850625}{256}=-139425+\frac{17850625}{256}$$

-139425 ni \frac{17850625}{256} ga qo'shish.

$$x^{2}-\frac{4225}{8}x+\frac{17850625}{256}=-\frac{17842175}{256}$$

x^{2}-\frac{4225}{8}x+\frac{17850625}{256} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{4225}{16}\right)^{2}=-\frac{17842175}{256}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{4225}{16}\right)^{2}}=\sqrt{-\frac{17842175}{256}}$$

Qisqartirish.

$$x-\frac{4225}{16}=\frac{65\sqrt{4223}i}{16} x-\frac{4225}{16}=-\frac{65\sqrt{4223}i}{16}$$

\frac{4225}{16} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{4225+65\sqrt{4223}i}{16} x=\frac{-65\sqrt{4223}i+4225}{16}$$