5975x^2+450125x-706653125=0 eching

$$5975 x ^ { 2 } + 450125 x - 706653125 = 0$$

x uchun yechish

$$x = \frac{5 \sqrt{1093863821} - 18005}{478} \approx 308,290922127$$

$$x=\frac{-5\sqrt{1093863821}-18005}{478}\approx -383,62565016$$

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.

$$5975x^{2}+450125x-706653125=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5975 ni a, 450125 ni b va -706653125 ni c bilan almashtiring.

$$x=\frac{-450125±\sqrt{450125^{2}-4\times 5975\left(-706653125\right)}}{2\times 5975}$$

450125 kvadratini chiqarish.

$$x=\frac{-450125±\sqrt{202612515625-4\times 5975\left(-706653125\right)}}{2\times 5975}$$

-4 ni 5975 marotabaga ko'paytirish.

$$x=\frac{-450125±\sqrt{202612515625-23900\left(-706653125\right)}}{2\times 5975}$$

-23900 ni -706653125 marotabaga ko'paytirish.

$$x=\frac{-450125±\sqrt{202612515625+16889009687500}}{2\times 5975}$$

202612515625 ni 16889009687500 ga qo'shish.

$$x=\frac{-450125±\sqrt{17091622203125}}{2\times 5975}$$

17091622203125 ning kvadrat ildizini chiqarish.

$$x=\frac{-450125±125\sqrt{1093863821}}{2\times 5975}$$

2 ni 5975 marotabaga ko'paytirish.

$$x=\frac{-450125±125\sqrt{1093863821}}{11950}$$

x=\frac{-450125±125\sqrt{1093863821}}{11950} tenglamasini yeching, bunda ± musbat. -450125 ni 125\sqrt{1093863821} ga qo'shish.

$$x=\frac{125\sqrt{1093863821}-450125}{11950}$$

-450125+125\sqrt{1093863821} ni 11950 ga bo'lish.

$$x=\frac{5\sqrt{1093863821}-18005}{478}$$

x=\frac{-450125±125\sqrt{1093863821}}{11950} tenglamasini yeching, bunda ± manfiy. -450125 dan 125\sqrt{1093863821} ni ayirish.

$$x=\frac{-125\sqrt{1093863821}-450125}{11950}$$

-450125-125\sqrt{1093863821} ni 11950 ga bo'lish.

$$x=\frac{-5\sqrt{1093863821}-18005}{478}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{1093863821}-18005}{478} x=\frac{-5\sqrt{1093863821}-18005}{478}$$

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.

$$5975x^{2}+450125x-706653125=0$$

706653125 ni tenglamaning ikkala tarafiga qo'shish.

$$5975x^{2}+450125x-706653125-\left(-706653125\right)=-\left(-706653125\right)$$

O‘zidan -706653125 ayirilsa 0 qoladi.

$$5975x^{2}+450125x=-\left(-706653125\right)$$

0 dan -706653125 ni ayirish.

$$5975x^{2}+450125x=706653125$$

Ikki tarafini 5975 ga bo‘ling.

$$\frac{5975x^{2}+450125x}{5975}=\frac{706653125}{5975}$$

5975 ga bo'lish 5975 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{450125}{5975}x=\frac{706653125}{5975}$$

\frac{450125}{5975} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{18005}{239}x=\frac{706653125}{5975}$$

\frac{706653125}{5975} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{18005}{239}x=\frac{28266125}{239}$$

\frac{18005}{239} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{18005}{478} olish uchun. Keyin, \frac{18005}{478} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{18005}{239}x+\left(\frac{18005}{478}\right)^{2}=\frac{28266125}{239}+\left(\frac{18005}{478}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{18005}{478} kvadratini chiqarish.

$$x^{2}+\frac{18005}{239}x+\frac{324180025}{228484}=\frac{28266125}{239}+\frac{324180025}{228484}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{28266125}{239} ni \frac{324180025}{228484} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{18005}{239}x+\frac{324180025}{228484}=\frac{27346595525}{228484}$$

x^{2}+\frac{18005}{239}x+\frac{324180025}{228484} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{18005}{478}\right)^{2}=\frac{27346595525}{228484}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{18005}{478}\right)^{2}}=\sqrt{\frac{27346595525}{228484}}$$

Qisqartirish.

$$x+\frac{18005}{478}=\frac{5\sqrt{1093863821}}{478} x+\frac{18005}{478}=-\frac{5\sqrt{1093863821}}{478}$$

Tenglamaning ikkala tarafidan \frac{18005}{478} ni ayirish.

$$x=\frac{5\sqrt{1093863821}-18005}{478} x=\frac{-5\sqrt{1093863821}-18005}{478}$$