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

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

x uchun yechish

$$x=76$$

$$x=1126$$

Kvadrat tenglamalaridan foydalanish qoidalari

85576 hosil qilish uchun 1126 va 76 ni ko'paytirish.

$$85576=\left(76+1126-x\right)x$$

1202 olish uchun 76 va 1126'ni qo'shing.

$$85576=\left(1202-x\right)x$$

1202-x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$85576=1202x-x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1202x-x^{2}=85576$$

Ikkala tarafdan 85576 ni ayirish.

$$1202x-x^{2}-85576=0$$

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.

$$-x^{2}+1202x-85576=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 1202 ni b va -85576 ni c bilan almashtiring.

$$x=\frac{-1202±\sqrt{1202^{2}-4\left(-1\right)\left(-85576\right)}}{2\left(-1\right)}$$

1202 kvadratini chiqarish.

$$x=\frac{-1202±\sqrt{1444804-4\left(-1\right)\left(-85576\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1202±\sqrt{1444804+4\left(-85576\right)}}{2\left(-1\right)}$$

4 ni -85576 marotabaga ko'paytirish.

$$x=\frac{-1202±\sqrt{1444804-342304}}{2\left(-1\right)}$$

1444804 ni -342304 ga qo'shish.

$$x=\frac{-1202±\sqrt{1102500}}{2\left(-1\right)}$$

1102500 ning kvadrat ildizini chiqarish.

$$x=\frac{-1202±1050}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1202±1050}{-2}$$

x=\frac{-1202±1050}{-2} tenglamasini yeching, bunda ± musbat. -1202 ni 1050 ga qo'shish.

$$x=-\frac{152}{-2}$$

-152 ni -2 ga bo'lish.

$$x=76$$

x=\frac{-1202±1050}{-2} tenglamasini yeching, bunda ± manfiy. -1202 dan 1050 ni ayirish.

$$x=-\frac{2252}{-2}$$

-2252 ni -2 ga bo'lish.

$$x=1126$$

Tenglama yechildi.

$$x=76 x=1126$$

Kvadratni yakunlash bo'yicha qadamlar

85576 hosil qilish uchun 1126 va 76 ni ko'paytirish.

$$85576=\left(76+1126-x\right)x$$

1202 olish uchun 76 va 1126'ni qo'shing.

$$85576=\left(1202-x\right)x$$

1202-x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$85576=1202x-x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1202x-x^{2}=85576$$

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

$$-x^{2}+1202x=85576$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+1202x}{-1}=\frac{85576}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1202}{-1}x=\frac{85576}{-1}$$

1202 ni -1 ga bo'lish.

$$x^{2}-1202x=\frac{85576}{-1}$$

85576 ni -1 ga bo'lish.

$$x^{2}-1202x=-85576$$

-1202 ni bo‘lish, x shartining koeffitsienti, 2 ga -601 olish uchun. Keyin, -601 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-1202x+\left(-601\right)^{2}=-85576+\left(-601\right)^{2}$$

-601 kvadratini chiqarish.

$$x^{2}-1202x+361201=-85576+361201$$

-85576 ni 361201 ga qo'shish.

$$x^{2}-1202x+361201=275625$$

x^{2}-1202x+361201 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-601\right)^{2}=275625$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-601\right)^{2}}=\sqrt{275625}$$

Qisqartirish.

$$x-601=525 x-601=-525$$

601 ni tenglamaning ikkala tarafiga qo'shish.

$$x=1126 x=76$$