3x^2-50x-26=0 eching

$$3 { x }^{ 2 } -50x-26=0$$

x uchun yechish

$$x = \frac{\sqrt{703} + 25}{3} \approx 17,171382389$$

$$x=\frac{25-\sqrt{703}}{3}\approx -0,504715722$$

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.

$$3x^{2}-50x-26=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -50 ni b va -26 ni c bilan almashtiring.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 3\left(-26\right)}}{2\times 3}$$

-50 kvadratini chiqarish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 3\left(-26\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-12\left(-26\right)}}{2\times 3}$$

-12 ni -26 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500+312}}{2\times 3}$$

2500 ni 312 ga qo'shish.

$$x=\frac{-\left(-50\right)±\sqrt{2812}}{2\times 3}$$

2812 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-50\right)±2\sqrt{703}}{2\times 3}$$

-50 ning teskarisi 50 ga teng.

$$x=\frac{50±2\sqrt{703}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{50±2\sqrt{703}}{6}$$

x=\frac{50±2\sqrt{703}}{6} tenglamasini yeching, bunda ± musbat. 50 ni 2\sqrt{703} ga qo'shish.

$$x=\frac{2\sqrt{703}+50}{6}$$

50+2\sqrt{703} ni 6 ga bo'lish.

$$x=\frac{\sqrt{703}+25}{3}$$

x=\frac{50±2\sqrt{703}}{6} tenglamasini yeching, bunda ± manfiy. 50 dan 2\sqrt{703} ni ayirish.

$$x=\frac{50-2\sqrt{703}}{6}$$

50-2\sqrt{703} ni 6 ga bo'lish.

$$x=\frac{25-\sqrt{703}}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{703}+25}{3} x=\frac{25-\sqrt{703}}{3}$$

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.

$$3x^{2}-50x-26=0$$

26 ni tenglamaning ikkala tarafiga qo'shish.

$$3x^{2}-50x-26-\left(-26\right)=-\left(-26\right)$$

O‘zidan -26 ayirilsa 0 qoladi.

$$3x^{2}-50x=-\left(-26\right)$$

0 dan -26 ni ayirish.

$$3x^{2}-50x=26$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-50x}{3}=\frac{26}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{50}{3}x=\frac{26}{3}$$

-\frac{50}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{25}{3} olish uchun. Keyin, -\frac{25}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{50}{3}x+\left(-\frac{25}{3}\right)^{2}=\frac{26}{3}+\left(-\frac{25}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{25}{3} kvadratini chiqarish.

$$x^{2}-\frac{50}{3}x+\frac{625}{9}=\frac{26}{3}+\frac{625}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{26}{3} ni \frac{625}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{50}{3}x+\frac{625}{9}=\frac{703}{9}$$

x^{2}-\frac{50}{3}x+\frac{625}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{25}{3}\right)^{2}=\frac{703}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{25}{3}\right)^{2}}=\sqrt{\frac{703}{9}}$$

Qisqartirish.

$$x-\frac{25}{3}=\frac{\sqrt{703}}{3} x-\frac{25}{3}=-\frac{\sqrt{703}}{3}$$

\frac{25}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{703}+25}{3} x=\frac{25-\sqrt{703}}{3}$$