3x^2-149*2x+400=0 eching

$$3 x ^ { 2 } - 149 \times 2 x + 400 = 0$$

x uchun yechish

$$x = \frac{\sqrt{21001} + 149}{3} \approx 97,972405916$$

$$x = \frac{149 - \sqrt{21001}}{3} \approx 1,360927417$$

Kvadrat tenglamalaridan foydalanish qoidalari

298 hosil qilish uchun 149 va 2 ni ko'paytirish.

$$3x^{2}-298x+400=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -298 ni b va 400 ni c bilan almashtiring.

$$x=\frac{-\left(-298\right)±\sqrt{\left(-298\right)^{2}-4\times 3\times 400}}{2\times 3}$$

-298 kvadratini chiqarish.

$$x=\frac{-\left(-298\right)±\sqrt{88804-4\times 3\times 400}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-298\right)±\sqrt{88804-12\times 400}}{2\times 3}$$

-12 ni 400 marotabaga ko'paytirish.

$$x=\frac{-\left(-298\right)±\sqrt{88804-4800}}{2\times 3}$$

88804 ni -4800 ga qo'shish.

$$x=\frac{-\left(-298\right)±\sqrt{84004}}{2\times 3}$$

84004 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-298\right)±2\sqrt{21001}}{2\times 3}$$

-298 ning teskarisi 298 ga teng.

$$x=\frac{298±2\sqrt{21001}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{298±2\sqrt{21001}}{6}$$

x=\frac{298±2\sqrt{21001}}{6} tenglamasini yeching, bunda ± musbat. 298 ni 2\sqrt{21001} ga qo'shish.

$$x=\frac{2\sqrt{21001}+298}{6}$$

298+2\sqrt{21001} ni 6 ga bo'lish.

$$x=\frac{\sqrt{21001}+149}{3}$$

x=\frac{298±2\sqrt{21001}}{6} tenglamasini yeching, bunda ± manfiy. 298 dan 2\sqrt{21001} ni ayirish.

$$x=\frac{298-2\sqrt{21001}}{6}$$

298-2\sqrt{21001} ni 6 ga bo'lish.

$$x=\frac{149-\sqrt{21001}}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{21001}+149}{3} x=\frac{149-\sqrt{21001}}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

298 hosil qilish uchun 149 va 2 ni ko'paytirish.

$$3x^{2}-298x+400=0$$

Ikkala tarafdan 400 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$3x^{2}-298x=-400$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-298x}{3}=-\frac{400}{3}$$

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

$$x^{2}-\frac{298}{3}x=-\frac{400}{3}$$

-\frac{298}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{149}{3} olish uchun. Keyin, -\frac{149}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{298}{3}x+\left(-\frac{149}{3}\right)^{2}=-\frac{400}{3}+\left(-\frac{149}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{149}{3} kvadratini chiqarish.

$$x^{2}-\frac{298}{3}x+\frac{22201}{9}=-\frac{400}{3}+\frac{22201}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{400}{3} ni \frac{22201}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{298}{3}x+\frac{22201}{9}=\frac{21001}{9}$$

x^{2}-\frac{298}{3}x+\frac{22201}{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.

$$\left(x-\frac{149}{3}\right)^{2}=\frac{21001}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{149}{3}\right)^{2}}=\sqrt{\frac{21001}{9}}$$

Qisqartirish.

$$x-\frac{149}{3}=\frac{\sqrt{21001}}{3} x-\frac{149}{3}=-\frac{\sqrt{21001}}{3}$$

\frac{149}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{21001}+149}{3} x=\frac{149-\sqrt{21001}}{3}$$