780x^2-28600x-38200=0 eching

$$780 { x }^{ 2 } -28600x-38200=0$$

x uchun yechish

$$x=\frac{\sqrt{585715}}{39}+\frac{55}{3}\approx 37,956928062$$

$$x=-\frac{\sqrt{585715}}{39}+\frac{55}{3}\approx -1,290261396$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$780x^{2}-28600x-38200=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 780 ni a, -28600 ni b va -38200 ni c bilan almashtiring.

$$x=\frac{-\left(-28600\right)±\sqrt{\left(-28600\right)^{2}-4\times 780\left(-38200\right)}}{2\times 780}$$

-28600 kvadratini chiqarish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-4\times 780\left(-38200\right)}}{2\times 780}$$

-4 ni 780 marotabaga ko'paytirish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-3120\left(-38200\right)}}{2\times 780}$$

-3120 ni -38200 marotabaga ko'paytirish.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000+119184000}}{2\times 780}$$

817960000 ni 119184000 ga qo'shish.

$$x=\frac{-\left(-28600\right)±\sqrt{937144000}}{2\times 780}$$

937144000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-28600\right)±40\sqrt{585715}}{2\times 780}$$

-28600 ning teskarisi 28600 ga teng.

$$x=\frac{28600±40\sqrt{585715}}{2\times 780}$$

2 ni 780 marotabaga ko'paytirish.

$$x=\frac{28600±40\sqrt{585715}}{1560}$$

x=\frac{28600±40\sqrt{585715}}{1560} tenglamasini yeching, bunda ± musbat. 28600 ni 40\sqrt{585715} ga qo'shish.

$$x=\frac{40\sqrt{585715}+28600}{1560}$$

28600+40\sqrt{585715} ni 1560 ga bo'lish.

$$x=\frac{\sqrt{585715}}{39}+\frac{55}{3}$$

x=\frac{28600±40\sqrt{585715}}{1560} tenglamasini yeching, bunda ± manfiy. 28600 dan 40\sqrt{585715} ni ayirish.

$$x=\frac{28600-40\sqrt{585715}}{1560}$$

28600-40\sqrt{585715} ni 1560 ga bo'lish.

$$x=-\frac{\sqrt{585715}}{39}+\frac{55}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{585715}}{39}+\frac{55}{3} x=-\frac{\sqrt{585715}}{39}+\frac{55}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$780x^{2}-28600x-38200=0$$

38200 ni tenglamaning ikkala tarafiga qo'shish.

$$780x^{2}-28600x-38200-\left(-38200\right)=-\left(-38200\right)$$

O‘zidan -38200 ayirilsa 0 qoladi.

$$780x^{2}-28600x=-\left(-38200\right)$$

0 dan -38200 ni ayirish.

$$780x^{2}-28600x=38200$$

Ikki tarafini 780 ga bo‘ling.

$$\frac{780x^{2}-28600x}{780}=\frac{38200}{780}$$

780 ga bo'lish 780 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{28600}{780}\right)x=\frac{38200}{780}$$

\frac{-28600}{780} ulushini 260 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{110}{3}x=\frac{38200}{780}$$

\frac{38200}{780} ulushini 20 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{110}{3}x=\frac{1910}{39}$$

-\frac{110}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{55}{3} olish uchun. Keyin, -\frac{55}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{110}{3}x+\left(-\frac{55}{3}\right)^{2}=\frac{1910}{39}+\left(-\frac{55}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{55}{3} kvadratini chiqarish.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=\frac{1910}{39}+\frac{3025}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1910}{39} ni \frac{3025}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=\frac{45055}{117}$$

x^{2}-\frac{110}{3}x+\frac{3025}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{55}{3}\right)^{2}=\frac{45055}{117}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{55}{3}\right)^{2}}=\sqrt{\frac{45055}{117}}$$

Qisqartirish.

$$x-\frac{55}{3}=\frac{\sqrt{585715}}{39} x-\frac{55}{3}=-\frac{\sqrt{585715}}{39}$$

\frac{55}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{585715}}{39}+\frac{55}{3} x=-\frac{\sqrt{585715}}{39}+\frac{55}{3}$$