3x^2=2x+12 eching

$$3 x ^ { 2 } = 2 x + 12$$

x uchun yechish

$$x = \frac{\sqrt{37} + 1}{3} \approx 2,360920843$$

$$x=\frac{1-\sqrt{37}}{3}\approx -1,694254177$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

$$3x^{2}-2x=12$$

Ikkala tarafdan 12 ni ayirish.

$$3x^{2}-2x-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -2 ni b va -12 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 3\left(-12\right)}}{2\times 3}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 3\left(-12\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4-12\left(-12\right)}}{2\times 3}$$

-12 ni -12 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+144}}{2\times 3}$$

4 ni 144 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{148}}{2\times 3}$$

148 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{37}}{2\times 3}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{37}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{37}}{6}$$

x=\frac{2±2\sqrt{37}}{6} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{37} ga qo'shish.

$$x=\frac{2\sqrt{37}+2}{6}$$

2+2\sqrt{37} ni 6 ga bo'lish.

$$x=\frac{\sqrt{37}+1}{3}$$

x=\frac{2±2\sqrt{37}}{6} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{37} ni ayirish.

$$x=\frac{2-2\sqrt{37}}{6}$$

2-2\sqrt{37} ni 6 ga bo'lish.

$$x=\frac{1-\sqrt{37}}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{37}+1}{3} x=\frac{1-\sqrt{37}}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

$$3x^{2}-2x=12$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-2x}{3}=\frac{12}{3}$$

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

$$x^{2}-\frac{2}{3}x=\frac{12}{3}$$

12 ni 3 ga bo'lish.

$$x^{2}-\frac{2}{3}x=4$$

-\frac{2}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{3} olish uchun. Keyin, -\frac{1}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{2}{3}x+\left(-\frac{1}{3}\right)^{2}=4+\left(-\frac{1}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{3} kvadratini chiqarish.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=4+\frac{1}{9}$$

4 ni \frac{1}{9} ga qo'shish.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{37}{9}$$

x^{2}-\frac{2}{3}x+\frac{1}{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.

$$\left(x-\frac{1}{3}\right)^{2}=\frac{37}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{3}\right)^{2}}=\sqrt{\frac{37}{9}}$$

Qisqartirish.

$$x-\frac{1}{3}=\frac{\sqrt{37}}{3} x-\frac{1}{3}=-\frac{\sqrt{37}}{3}$$

\frac{1}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{37}+1}{3} x=\frac{1-\sqrt{37}}{3}$$