76+x*(1126-x)=x*x eching

$$76+x \times (1126-x)=x \times x$$

x uchun yechish

$$x = \frac{\sqrt{317121} + 563}{2} \approx 563,06748747$$

$$x=\frac{563-\sqrt{317121}}{2}\approx -0,06748747$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$76+x\left(1126-x\right)=x^{2}$$

x ga 1126-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$76+1126x-x^{2}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$76+1126x-x^{2}-x^{2}=0$$

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

$$76+1126x-2x^{2}=0$$

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.

$$-2x^{2}+1126x+76=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 1126 ni b va 76 ni c bilan almashtiring.

$$x=\frac{-1126±\sqrt{1126^{2}-4\left(-2\right)\times 76}}{2\left(-2\right)}$$

1126 kvadratini chiqarish.

$$x=\frac{-1126±\sqrt{1267876-4\left(-2\right)\times 76}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-1126±\sqrt{1267876+8\times 76}}{2\left(-2\right)}$$

8 ni 76 marotabaga ko'paytirish.

$$x=\frac{-1126±\sqrt{1267876+608}}{2\left(-2\right)}$$

1267876 ni 608 ga qo'shish.

$$x=\frac{-1126±\sqrt{1268484}}{2\left(-2\right)}$$

1268484 ning kvadrat ildizini chiqarish.

$$x=\frac{-1126±2\sqrt{317121}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-1126±2\sqrt{317121}}{-4}$$

x=\frac{-1126±2\sqrt{317121}}{-4} tenglamasini yeching, bunda ± musbat. -1126 ni 2\sqrt{317121} ga qo'shish.

$$x=\frac{2\sqrt{317121}-1126}{-4}$$

-1126+2\sqrt{317121} ni -4 ga bo'lish.

$$x=\frac{563-\sqrt{317121}}{2}$$

x=\frac{-1126±2\sqrt{317121}}{-4} tenglamasini yeching, bunda ± manfiy. -1126 dan 2\sqrt{317121} ni ayirish.

$$x=\frac{-2\sqrt{317121}-1126}{-4}$$

-1126-2\sqrt{317121} ni -4 ga bo'lish.

$$x=\frac{\sqrt{317121}+563}{2}$$

Tenglama yechildi.

$$x=\frac{563-\sqrt{317121}}{2} x=\frac{\sqrt{317121}+563}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$76+x\left(1126-x\right)=x^{2}$$

x ga 1126-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$76+1126x-x^{2}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$76+1126x-x^{2}-x^{2}=0$$

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

$$76+1126x-2x^{2}=0$$

Ikkala tarafdan 76 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$1126x-2x^{2}=-76$$

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

$$-2x^{2}+1126x=-76$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+1126x}{-2}=-\frac{76}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1126}{-2}x=-\frac{76}{-2}$$

1126 ni -2 ga bo'lish.

$$x^{2}-563x=-\frac{76}{-2}$$

-76 ni -2 ga bo'lish.

$$x^{2}-563x=38$$

-563 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{563}{2} olish uchun. Keyin, -\frac{563}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-563x+\left(-\frac{563}{2}\right)^{2}=38+\left(-\frac{563}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{563}{2} kvadratini chiqarish.

$$x^{2}-563x+\frac{316969}{4}=38+\frac{316969}{4}$$

38 ni \frac{316969}{4} ga qo'shish.

$$x^{2}-563x+\frac{316969}{4}=\frac{317121}{4}$$

x^{2}-563x+\frac{316969}{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.

$$\left(x-\frac{563}{2}\right)^{2}=\frac{317121}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{563}{2}\right)^{2}}=\sqrt{\frac{317121}{4}}$$

Qisqartirish.

$$x-\frac{563}{2}=\frac{\sqrt{317121}}{2} x-\frac{563}{2}=-\frac{\sqrt{317121}}{2}$$

\frac{563}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{317121}+563}{2} x=\frac{563-\sqrt{317121}}{2}$$