x^2=(x-10)+24^2 eching

$$x ^ { 2 } = ( x - 10 ) + 24 ^ { 2 }$$

x uchun yechish

$$x = \frac{\sqrt{2265} + 1}{2} \approx 24,296008069$$

$$x=\frac{1-\sqrt{2265}}{2}\approx -23,296008069$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 24 ga hisoblang va 576 ni qiymatni oling.

$$x^{2}=x-10+576$$

566 olish uchun -10 va 576'ni qo'shing.

$$x^{2}=x+566$$

Ikkala tarafdan x ni ayirish.

$$x^{2}-x=566$$

Ikkala tarafdan 566 ni ayirish.

$$x^{2}-x-566=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1 ni b va -566 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-566\right)}}{2}$$

-4 ni -566 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+2264}}{2}$$

1 ni 2264 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{2265}}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{2265}}{2}$$

x=\frac{1±\sqrt{2265}}{2} tenglamasini yeching, bunda ± musbat. 1 ni \sqrt{2265} ga qo'shish.

$$x=\frac{\sqrt{2265}+1}{2}$$

x=\frac{1±\sqrt{2265}}{2} tenglamasini yeching, bunda ± manfiy. 1 dan \sqrt{2265} ni ayirish.

$$x=\frac{1-\sqrt{2265}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{2265}+1}{2} x=\frac{1-\sqrt{2265}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2 daraja ko‘rsatkichini 24 ga hisoblang va 576 ni qiymatni oling.

$$x^{2}=x-10+576$$

566 olish uchun -10 va 576'ni qo'shing.

$$x^{2}=x+566$$

Ikkala tarafdan x ni ayirish.

$$x^{2}-x=566$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=566+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=566+\frac{1}{4}$$

566 ni \frac{1}{4} ga qo'shish.

$$x^{2}-x+\frac{1}{4}=\frac{2265}{4}$$

x^{2}-x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{2265}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{2265}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{\sqrt{2265}}{2} x-\frac{1}{2}=-\frac{\sqrt{2265}}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{2265}+1}{2} x=\frac{1-\sqrt{2265}}{2}$$