x^2+76x-76*1126=0 eching

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

x uchun yechish

$$x=2\sqrt{21755}-38\approx 256,991525302$$

$$x=-2\sqrt{21755}-38\approx -332,991525302$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}+76x-85576=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 76 ni b va -85576 ni c bilan almashtiring.

$$x=\frac{-76±\sqrt{76^{2}-4\left(-85576\right)}}{2}$$

76 kvadratini chiqarish.

$$x=\frac{-76±\sqrt{5776-4\left(-85576\right)}}{2}$$

-4 ni -85576 marotabaga ko'paytirish.

$$x=\frac{-76±\sqrt{5776+342304}}{2}$$

5776 ni 342304 ga qo'shish.

$$x=\frac{-76±\sqrt{348080}}{2}$$

348080 ning kvadrat ildizini chiqarish.

$$x=\frac{-76±4\sqrt{21755}}{2}$$

x=\frac{-76±4\sqrt{21755}}{2} tenglamasini yeching, bunda ± musbat. -76 ni 4\sqrt{21755} ga qo'shish.

$$x=\frac{4\sqrt{21755}-76}{2}$$

-76+4\sqrt{21755} ni 2 ga bo'lish.

$$x=2\sqrt{21755}-38$$

x=\frac{-76±4\sqrt{21755}}{2} tenglamasini yeching, bunda ± manfiy. -76 dan 4\sqrt{21755} ni ayirish.

$$x=\frac{-4\sqrt{21755}-76}{2}$$

-76-4\sqrt{21755} ni 2 ga bo'lish.

$$x=-2\sqrt{21755}-38$$

Tenglama yechildi.

$$x=2\sqrt{21755}-38 x=-2\sqrt{21755}-38$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}+76x-85576=0$$

85576 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}+76x=85576$$

76 ni bo‘lish, x shartining koeffitsienti, 2 ga 38 olish uchun. Keyin, 38 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+76x+38^{2}=85576+38^{2}$$

38 kvadratini chiqarish.

$$x^{2}+76x+1444=85576+1444$$

85576 ni 1444 ga qo'shish.

$$x^{2}+76x+1444=87020$$

x^{2}+76x+1444 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+38\right)^{2}=87020$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+38\right)^{2}}=\sqrt{87020}$$

Qisqartirish.

$$x+38=2\sqrt{21755} x+38=-2\sqrt{21755}$$

Tenglamaning ikkala tarafidan 38 ni ayirish.

$$x=2\sqrt{21755}-38 x=-2\sqrt{21755}-38$$