38706x^2-41070x+9027=0 eching

$$38706 x ^ { 2 } - 41070 x + 9027 = 0$$

x uchun yechish

$$x=\frac{\sqrt{8031907}+6845}{12902}\approx 0,750198568$$

$$x=\frac{6845-\sqrt{8031907}}{12902}\approx 0,310877234$$

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.

$$38706x^{2}-41070x+9027=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 38706 ni a, -41070 ni b va 9027 ni c bilan almashtiring.

$$x=\frac{-\left(-41070\right)±\sqrt{\left(-41070\right)^{2}-4\times 38706\times 9027}}{2\times 38706}$$

-41070 kvadratini chiqarish.

$$x=\frac{-\left(-41070\right)±\sqrt{1686744900-4\times 38706\times 9027}}{2\times 38706}$$

-4 ni 38706 marotabaga ko'paytirish.

$$x=\frac{-\left(-41070\right)±\sqrt{1686744900-154824\times 9027}}{2\times 38706}$$

-154824 ni 9027 marotabaga ko'paytirish.

$$x=\frac{-\left(-41070\right)±\sqrt{1686744900-1397596248}}{2\times 38706}$$

1686744900 ni -1397596248 ga qo'shish.

$$x=\frac{-\left(-41070\right)±\sqrt{289148652}}{2\times 38706}$$

289148652 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-41070\right)±6\sqrt{8031907}}{2\times 38706}$$

-41070 ning teskarisi 41070 ga teng.

$$x=\frac{41070±6\sqrt{8031907}}{2\times 38706}$$

2 ni 38706 marotabaga ko'paytirish.

$$x=\frac{41070±6\sqrt{8031907}}{77412}$$

x=\frac{41070±6\sqrt{8031907}}{77412} tenglamasini yeching, bunda ± musbat. 41070 ni 6\sqrt{8031907} ga qo'shish.

$$x=\frac{6\sqrt{8031907}+41070}{77412}$$

41070+6\sqrt{8031907} ni 77412 ga bo'lish.

$$x=\frac{\sqrt{8031907}+6845}{12902}$$

x=\frac{41070±6\sqrt{8031907}}{77412} tenglamasini yeching, bunda ± manfiy. 41070 dan 6\sqrt{8031907} ni ayirish.

$$x=\frac{41070-6\sqrt{8031907}}{77412}$$

41070-6\sqrt{8031907} ni 77412 ga bo'lish.

$$x=\frac{6845-\sqrt{8031907}}{12902}$$

Tenglama yechildi.

$$x=\frac{\sqrt{8031907}+6845}{12902} x=\frac{6845-\sqrt{8031907}}{12902}$$

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.

$$38706x^{2}-41070x+9027=0$$

Tenglamaning ikkala tarafidan 9027 ni ayirish.

$$38706x^{2}-41070x+9027-9027=-9027$$

O‘zidan 9027 ayirilsa 0 qoladi.

$$38706x^{2}-41070x=-9027$$

Ikki tarafini 38706 ga bo‘ling.

$$\frac{38706x^{2}-41070x}{38706}=-\frac{9027}{38706}$$

38706 ga bo'lish 38706 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{41070}{38706}\right)x=-\frac{9027}{38706}$$

\frac{-41070}{38706} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{6845}{6451}x=-\frac{9027}{38706}$$

\frac{-9027}{38706} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{6845}{6451}x=-\frac{3009}{12902}$$

-\frac{6845}{6451} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{6845}{12902} olish uchun. Keyin, -\frac{6845}{12902} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{6845}{6451}x+\left(-\frac{6845}{12902}\right)^{2}=-\frac{3009}{12902}+\left(-\frac{6845}{12902}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{6845}{12902} kvadratini chiqarish.

$$x^{2}-\frac{6845}{6451}x+\frac{46854025}{166461604}=-\frac{3009}{12902}+\frac{46854025}{166461604}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{3009}{12902} ni \frac{46854025}{166461604} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{6845}{6451}x+\frac{46854025}{166461604}=\frac{8031907}{166461604}$$

x^{2}-\frac{6845}{6451}x+\frac{46854025}{166461604} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{6845}{12902}\right)^{2}=\frac{8031907}{166461604}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{6845}{12902}\right)^{2}}=\sqrt{\frac{8031907}{166461604}}$$

Qisqartirish.

$$x-\frac{6845}{12902}=\frac{\sqrt{8031907}}{12902} x-\frac{6845}{12902}=-\frac{\sqrt{8031907}}{12902}$$

\frac{6845}{12902} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{8031907}+6845}{12902} x=\frac{6845-\sqrt{8031907}}{12902}$$