301x^2-918x=256 eching

$$301 x ^ { 2 } - 918 x = 256$$

x uchun yechish

$$x = \frac{\sqrt{287737} + 459}{301} \approx 3,307014029$$

$$x=\frac{459-\sqrt{287737}}{301}\approx -0,257180142$$

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.

$$301x^{2}-918x=256$$

Tenglamaning ikkala tarafidan 256 ni ayirish.

$$301x^{2}-918x-256=256-256$$

O‘zidan 256 ayirilsa 0 qoladi.

$$301x^{2}-918x-256=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 301 ni a, -918 ni b va -256 ni c bilan almashtiring.

$$x=\frac{-\left(-918\right)±\sqrt{\left(-918\right)^{2}-4\times 301\left(-256\right)}}{2\times 301}$$

-918 kvadratini chiqarish.

$$x=\frac{-\left(-918\right)±\sqrt{842724-4\times 301\left(-256\right)}}{2\times 301}$$

-4 ni 301 marotabaga ko'paytirish.

$$x=\frac{-\left(-918\right)±\sqrt{842724-1204\left(-256\right)}}{2\times 301}$$

-1204 ni -256 marotabaga ko'paytirish.

$$x=\frac{-\left(-918\right)±\sqrt{842724+308224}}{2\times 301}$$

842724 ni 308224 ga qo'shish.

$$x=\frac{-\left(-918\right)±\sqrt{1150948}}{2\times 301}$$

1150948 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-918\right)±2\sqrt{287737}}{2\times 301}$$

-918 ning teskarisi 918 ga teng.

$$x=\frac{918±2\sqrt{287737}}{2\times 301}$$

2 ni 301 marotabaga ko'paytirish.

$$x=\frac{918±2\sqrt{287737}}{602}$$

x=\frac{918±2\sqrt{287737}}{602} tenglamasini yeching, bunda ± musbat. 918 ni 2\sqrt{287737} ga qo'shish.

$$x=\frac{2\sqrt{287737}+918}{602}$$

918+2\sqrt{287737} ni 602 ga bo'lish.

$$x=\frac{\sqrt{287737}+459}{301}$$

x=\frac{918±2\sqrt{287737}}{602} tenglamasini yeching, bunda ± manfiy. 918 dan 2\sqrt{287737} ni ayirish.

$$x=\frac{918-2\sqrt{287737}}{602}$$

918-2\sqrt{287737} ni 602 ga bo'lish.

$$x=\frac{459-\sqrt{287737}}{301}$$

Tenglama yechildi.

$$x=\frac{\sqrt{287737}+459}{301} x=\frac{459-\sqrt{287737}}{301}$$

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.

$$301x^{2}-918x=256$$

Ikki tarafini 301 ga bo‘ling.

$$\frac{301x^{2}-918x}{301}=\frac{256}{301}$$

301 ga bo'lish 301 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{918}{301}x=\frac{256}{301}$$

-\frac{918}{301} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{459}{301} olish uchun. Keyin, -\frac{459}{301} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{918}{301}x+\left(-\frac{459}{301}\right)^{2}=\frac{256}{301}+\left(-\frac{459}{301}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{459}{301} kvadratini chiqarish.

$$x^{2}-\frac{918}{301}x+\frac{210681}{90601}=\frac{256}{301}+\frac{210681}{90601}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{256}{301} ni \frac{210681}{90601} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{918}{301}x+\frac{210681}{90601}=\frac{287737}{90601}$$

x^{2}-\frac{918}{301}x+\frac{210681}{90601} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{459}{301}\right)^{2}=\frac{287737}{90601}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{459}{301}\right)^{2}}=\sqrt{\frac{287737}{90601}}$$

Qisqartirish.

$$x-\frac{459}{301}=\frac{\sqrt{287737}}{301} x-\frac{459}{301}=-\frac{\sqrt{287737}}{301}$$

\frac{459}{301} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{287737}+459}{301} x=\frac{459-\sqrt{287737}}{301}$$