56=-32139x^2+13089x+71856 eching

$$56 = -32139 { x }^{ 2 } +13089x+71856$$

x uchun yechish

$$x = \frac{\sqrt{1044626969} + 4363}{21426} \approx 1,712110963$$

$$x=\frac{4363-\sqrt{1044626969}}{21426}\approx -1,304848758$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-32139x^{2}+13089x+71856=56$$

Ikkala tarafdan 56 ni ayirish.

$$-32139x^{2}+13089x+71856-56=0$$

71800 olish uchun 71856 dan 56 ni ayirish.

$$-32139x^{2}+13089x+71800=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -32139 ni a, 13089 ni b va 71800 ni c bilan almashtiring.

$$x=\frac{-13089±\sqrt{13089^{2}-4\left(-32139\right)\times 71800}}{2\left(-32139\right)}$$

13089 kvadratini chiqarish.

$$x=\frac{-13089±\sqrt{171321921-4\left(-32139\right)\times 71800}}{2\left(-32139\right)}$$

-4 ni -32139 marotabaga ko'paytirish.

$$x=\frac{-13089±\sqrt{171321921+128556\times 71800}}{2\left(-32139\right)}$$

128556 ni 71800 marotabaga ko'paytirish.

$$x=\frac{-13089±\sqrt{171321921+9230320800}}{2\left(-32139\right)}$$

171321921 ni 9230320800 ga qo'shish.

$$x=\frac{-13089±\sqrt{9401642721}}{2\left(-32139\right)}$$

9401642721 ning kvadrat ildizini chiqarish.

$$x=\frac{-13089±3\sqrt{1044626969}}{2\left(-32139\right)}$$

2 ni -32139 marotabaga ko'paytirish.

$$x=\frac{-13089±3\sqrt{1044626969}}{-64278}$$

x=\frac{-13089±3\sqrt{1044626969}}{-64278} tenglamasini yeching, bunda ± musbat. -13089 ni 3\sqrt{1044626969} ga qo'shish.

$$x=\frac{3\sqrt{1044626969}-13089}{-64278}$$

-13089+3\sqrt{1044626969} ni -64278 ga bo'lish.

$$x=\frac{4363-\sqrt{1044626969}}{21426}$$

x=\frac{-13089±3\sqrt{1044626969}}{-64278} tenglamasini yeching, bunda ± manfiy. -13089 dan 3\sqrt{1044626969} ni ayirish.

$$x=\frac{-3\sqrt{1044626969}-13089}{-64278}$$

-13089-3\sqrt{1044626969} ni -64278 ga bo'lish.

$$x=\frac{\sqrt{1044626969}+4363}{21426}$$

Tenglama yechildi.

$$x=\frac{4363-\sqrt{1044626969}}{21426} x=\frac{\sqrt{1044626969}+4363}{21426}$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-32139x^{2}+13089x+71856=56$$

Ikkala tarafdan 71856 ni ayirish.

$$-32139x^{2}+13089x=56-71856$$

-71800 olish uchun 56 dan 71856 ni ayirish.

$$-32139x^{2}+13089x=-71800$$

Ikki tarafini -32139 ga bo‘ling.

$$\frac{-32139x^{2}+13089x}{-32139}=-\frac{71800}{-32139}$$

-32139 ga bo'lish -32139 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{13089}{-32139}x=-\frac{71800}{-32139}$$

\frac{13089}{-32139} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{4363}{10713}x=-\frac{71800}{-32139}$$

-71800 ni -32139 ga bo'lish.

$$x^{2}-\frac{4363}{10713}x=\frac{71800}{32139}$$

-\frac{4363}{10713} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{4363}{21426} olish uchun. Keyin, -\frac{4363}{21426} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{4363}{10713}x+\left(-\frac{4363}{21426}\right)^{2}=\frac{71800}{32139}+\left(-\frac{4363}{21426}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{4363}{21426} kvadratini chiqarish.

$$x^{2}-\frac{4363}{10713}x+\frac{19035769}{459073476}=\frac{71800}{32139}+\frac{19035769}{459073476}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{71800}{32139} ni \frac{19035769}{459073476} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{4363}{10713}x+\frac{19035769}{459073476}=\frac{1044626969}{459073476}$$

x^{2}-\frac{4363}{10713}x+\frac{19035769}{459073476} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{4363}{21426}\right)^{2}=\frac{1044626969}{459073476}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{4363}{21426}\right)^{2}}=\sqrt{\frac{1044626969}{459073476}}$$

Qisqartirish.

$$x-\frac{4363}{21426}=\frac{\sqrt{1044626969}}{21426} x-\frac{4363}{21426}=-\frac{\sqrt{1044626969}}{21426}$$

\frac{4363}{21426} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{1044626969}+4363}{21426} x=\frac{4363-\sqrt{1044626969}}{21426}$$