6500=n[595-15n) eching

$$6500 = n [ 595 - 15 n )$$

n uchun yechish

$$n=\frac{119+\sqrt{1439}i}{6}\approx 19,833333333+6,322358913i$$

$$n=\frac{-\sqrt{1439}i+119}{6}\approx 19,833333333-6,322358913i$$

Kvadrat tenglamalaridan foydalanish qoidalari

n ga 595-15n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6500=595n-15n^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$595n-15n^{2}=6500$$

Ikkala tarafdan 6500 ni ayirish.

$$595n-15n^{2}-6500=0$$

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.

$$-15n^{2}+595n-6500=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -15 ni a, 595 ni b va -6500 ni c bilan almashtiring.

$$n=\frac{-595±\sqrt{595^{2}-4\left(-15\right)\left(-6500\right)}}{2\left(-15\right)}$$

595 kvadratini chiqarish.

$$n=\frac{-595±\sqrt{354025-4\left(-15\right)\left(-6500\right)}}{2\left(-15\right)}$$

-4 ni -15 marotabaga ko'paytirish.

$$n=\frac{-595±\sqrt{354025+60\left(-6500\right)}}{2\left(-15\right)}$$

60 ni -6500 marotabaga ko'paytirish.

$$n=\frac{-595±\sqrt{354025-390000}}{2\left(-15\right)}$$

354025 ni -390000 ga qo'shish.

$$n=\frac{-595±\sqrt{-35975}}{2\left(-15\right)}$$

-35975 ning kvadrat ildizini chiqarish.

$$n=\frac{-595±5\sqrt{1439}i}{2\left(-15\right)}$$

2 ni -15 marotabaga ko'paytirish.

$$n=\frac{-595±5\sqrt{1439}i}{-30}$$

n=\frac{-595±5\sqrt{1439}i}{-30} tenglamasini yeching, bunda ± musbat. -595 ni 5i\sqrt{1439} ga qo'shish.

$$n=\frac{-595+5\sqrt{1439}i}{-30}$$

-595+5i\sqrt{1439} ni -30 ga bo'lish.

$$n=\frac{-\sqrt{1439}i+119}{6}$$

n=\frac{-595±5\sqrt{1439}i}{-30} tenglamasini yeching, bunda ± manfiy. -595 dan 5i\sqrt{1439} ni ayirish.

$$n=\frac{-5\sqrt{1439}i-595}{-30}$$

-595-5i\sqrt{1439} ni -30 ga bo'lish.

$$n=\frac{119+\sqrt{1439}i}{6}$$

Tenglama yechildi.

$$n=\frac{-\sqrt{1439}i+119}{6} n=\frac{119+\sqrt{1439}i}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

n ga 595-15n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6500=595n-15n^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$595n-15n^{2}=6500$$

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

$$-15n^{2}+595n=6500$$

Ikki tarafini -15 ga bo‘ling.

$$\frac{-15n^{2}+595n}{-15}=\frac{6500}{-15}$$

-15 ga bo'lish -15 ga ko'paytirishni bekor qiladi.

$$n^{2}+\frac{595}{-15}n=\frac{6500}{-15}$$

\frac{595}{-15} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$n^{2}-\frac{119}{3}n=\frac{6500}{-15}$$

\frac{6500}{-15} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$n^{2}-\frac{119}{3}n=-\frac{1300}{3}$$

-\frac{119}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{119}{6} olish uchun. Keyin, -\frac{119}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-\frac{119}{3}n+\left(-\frac{119}{6}\right)^{2}=-\frac{1300}{3}+\left(-\frac{119}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{119}{6} kvadratini chiqarish.

$$n^{2}-\frac{119}{3}n+\frac{14161}{36}=-\frac{1300}{3}+\frac{14161}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1300}{3} ni \frac{14161}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$n^{2}-\frac{119}{3}n+\frac{14161}{36}=-\frac{1439}{36}$$

n^{2}-\frac{119}{3}n+\frac{14161}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n-\frac{119}{6}\right)^{2}=-\frac{1439}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{119}{6}\right)^{2}}=\sqrt{-\frac{1439}{36}}$$

Qisqartirish.

$$n-\frac{119}{6}=\frac{\sqrt{1439}i}{6} n-\frac{119}{6}=-\frac{\sqrt{1439}i}{6}$$

\frac{119}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{119+\sqrt{1439}i}{6} n=\frac{-\sqrt{1439}i+119}{6}$$