n^2+301258n-1205032=0 eching

$$n ^ { 2 } + 301258 n - 1205032 = 0$$

n uchun yechish

$$n=\sqrt{22690300673}-150629\approx 3,999946891$$

$$n=-\sqrt{22690300673}-150629\approx -301261,999946891$$

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.

$$n^{2}+301258n-1205032=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 301258 ni b va -1205032 ni c bilan almashtiring.

$$n=\frac{-301258±\sqrt{301258^{2}-4\left(-1205032\right)}}{2}$$

301258 kvadratini chiqarish.

$$n=\frac{-301258±\sqrt{90756382564-4\left(-1205032\right)}}{2}$$

-4 ni -1205032 marotabaga ko'paytirish.

$$n=\frac{-301258±\sqrt{90756382564+4820128}}{2}$$

90756382564 ni 4820128 ga qo'shish.

$$n=\frac{-301258±\sqrt{90761202692}}{2}$$

90761202692 ning kvadrat ildizini chiqarish.

$$n=\frac{-301258±2\sqrt{22690300673}}{2}$$

n=\frac{-301258±2\sqrt{22690300673}}{2} tenglamasini yeching, bunda ± musbat. -301258 ni 2\sqrt{22690300673} ga qo'shish.

$$n=\frac{2\sqrt{22690300673}-301258}{2}$$

-301258+2\sqrt{22690300673} ni 2 ga bo'lish.

$$n=\sqrt{22690300673}-150629$$

n=\frac{-301258±2\sqrt{22690300673}}{2} tenglamasini yeching, bunda ± manfiy. -301258 dan 2\sqrt{22690300673} ni ayirish.

$$n=\frac{-2\sqrt{22690300673}-301258}{2}$$

-301258-2\sqrt{22690300673} ni 2 ga bo'lish.

$$n=-\sqrt{22690300673}-150629$$

Tenglama yechildi.

$$n=\sqrt{22690300673}-150629 n=-\sqrt{22690300673}-150629$$

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.

$$n^{2}+301258n-1205032=0$$

1205032 ni tenglamaning ikkala tarafiga qo'shish.

$$n^{2}+301258n-1205032-\left(-1205032\right)=-\left(-1205032\right)$$

O‘zidan -1205032 ayirilsa 0 qoladi.

$$n^{2}+301258n=-\left(-1205032\right)$$

0 dan -1205032 ni ayirish.

$$n^{2}+301258n=1205032$$

301258 ni bo‘lish, x shartining koeffitsienti, 2 ga 150629 olish uchun. Keyin, 150629 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}+301258n+150629^{2}=1205032+150629^{2}$$

150629 kvadratini chiqarish.

$$n^{2}+301258n+22689095641=1205032+22689095641$$

1205032 ni 22689095641 ga qo'shish.

$$n^{2}+301258n+22689095641=22690300673$$

n^{2}+301258n+22689095641 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n+150629\right)^{2}=22690300673$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n+150629\right)^{2}}=\sqrt{22690300673}$$

Qisqartirish.

$$n+150629=\sqrt{22690300673} n+150629=-\sqrt{22690300673}$$

Tenglamaning ikkala tarafidan 150629 ni ayirish.

$$n=\sqrt{22690300673}-150629 n=-\sqrt{22690300673}-150629$$