7875x^2+1425x-1=0 eching

$$7875 { x }^{ 2 } +1425x-1=0$$

x uchun yechish

$$x=\frac{\sqrt{9165}}{1050}-\frac{19}{210}\approx 0,000699054$$

$$x=-\frac{\sqrt{9165}}{1050}-\frac{19}{210}\approx -0,181651435$$

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.

$$7875x^{2}+1425x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7875 ni a, 1425 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-1425±\sqrt{1425^{2}-4\times 7875\left(-1\right)}}{2\times 7875}$$

1425 kvadratini chiqarish.

$$x=\frac{-1425±\sqrt{2030625-4\times 7875\left(-1\right)}}{2\times 7875}$$

-4 ni 7875 marotabaga ko'paytirish.

$$x=\frac{-1425±\sqrt{2030625-31500\left(-1\right)}}{2\times 7875}$$

-31500 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1425±\sqrt{2030625+31500}}{2\times 7875}$$

2030625 ni 31500 ga qo'shish.

$$x=\frac{-1425±\sqrt{2062125}}{2\times 7875}$$

2062125 ning kvadrat ildizini chiqarish.

$$x=\frac{-1425±15\sqrt{9165}}{2\times 7875}$$

2 ni 7875 marotabaga ko'paytirish.

$$x=\frac{-1425±15\sqrt{9165}}{15750}$$

x=\frac{-1425±15\sqrt{9165}}{15750} tenglamasini yeching, bunda ± musbat. -1425 ni 15\sqrt{9165} ga qo'shish.

$$x=\frac{15\sqrt{9165}-1425}{15750}$$

-1425+15\sqrt{9165} ni 15750 ga bo'lish.

$$x=\frac{\sqrt{9165}}{1050}-\frac{19}{210}$$

x=\frac{-1425±15\sqrt{9165}}{15750} tenglamasini yeching, bunda ± manfiy. -1425 dan 15\sqrt{9165} ni ayirish.

$$x=\frac{-15\sqrt{9165}-1425}{15750}$$

-1425-15\sqrt{9165} ni 15750 ga bo'lish.

$$x=-\frac{\sqrt{9165}}{1050}-\frac{19}{210}$$

Tenglama yechildi.

$$x=\frac{\sqrt{9165}}{1050}-\frac{19}{210} x=-\frac{\sqrt{9165}}{1050}-\frac{19}{210}$$

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.

$$7875x^{2}+1425x-1=0$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$7875x^{2}+1425x-1-\left(-1\right)=-\left(-1\right)$$

O‘zidan -1 ayirilsa 0 qoladi.

$$7875x^{2}+1425x=-\left(-1\right)$$

0 dan -1 ni ayirish.

$$7875x^{2}+1425x=1$$

Ikki tarafini 7875 ga bo‘ling.

$$\frac{7875x^{2}+1425x}{7875}=\frac{1}{7875}$$

7875 ga bo'lish 7875 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1425}{7875}x=\frac{1}{7875}$$

\frac{1425}{7875} ulushini 75 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{19}{105}x=\frac{1}{7875}$$

\frac{19}{105} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{19}{210} olish uchun. Keyin, \frac{19}{210} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{19}{105}x+\left(\frac{19}{210}\right)^{2}=\frac{1}{7875}+\left(\frac{19}{210}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{19}{210} kvadratini chiqarish.

$$x^{2}+\frac{19}{105}x+\frac{361}{44100}=\frac{1}{7875}+\frac{361}{44100}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{7875} ni \frac{361}{44100} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{19}{105}x+\frac{361}{44100}=\frac{611}{73500}$$

x^{2}+\frac{19}{105}x+\frac{361}{44100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{19}{210}\right)^{2}=\frac{611}{73500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{19}{210}\right)^{2}}=\sqrt{\frac{611}{73500}}$$

Qisqartirish.

$$x+\frac{19}{210}=\frac{\sqrt{9165}}{1050} x+\frac{19}{210}=-\frac{\sqrt{9165}}{1050}$$

Tenglamaning ikkala tarafidan \frac{19}{210} ni ayirish.

$$x=\frac{\sqrt{9165}}{1050}-\frac{19}{210} x=-\frac{\sqrt{9165}}{1050}-\frac{19}{210}$$