4x^2+4x+2-2x^2-10x-8=0 eching

$$4 { x }^{ 2 } +4x+2-2 { x }^{ 2 } -10x-8=0$$

x uchun yechish

$$x = \frac{\sqrt{21} + 3}{2} \approx 3,791287847$$

$$x=\frac{3-\sqrt{21}}{2}\approx -0,791287847$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x^{2} ni olish uchun 4x^{2} va -2x^{2} ni birlashtirish.

$$2x^{2}+4x+2-10x-8=0$$

-6x ni olish uchun 4x va -10x ni birlashtirish.

$$2x^{2}-6x+2-8=0$$

-6 olish uchun 2 dan 8 ni ayirish.

$$2x^{2}-6x-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -6 ni b va -6 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 2\left(-6\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-8\left(-6\right)}}{2\times 2}$$

-8 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+48}}{2\times 2}$$

36 ni 48 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{84}}{2\times 2}$$

84 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{21}}{2\times 2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{21}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{6±2\sqrt{21}}{4}$$

x=\frac{6±2\sqrt{21}}{4} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{21} ga qo'shish.

$$x=\frac{2\sqrt{21}+6}{4}$$

6+2\sqrt{21} ni 4 ga bo'lish.

$$x=\frac{\sqrt{21}+3}{2}$$

x=\frac{6±2\sqrt{21}}{4} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{21} ni ayirish.

$$x=\frac{6-2\sqrt{21}}{4}$$

6-2\sqrt{21} ni 4 ga bo'lish.

$$x=\frac{3-\sqrt{21}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{21}+3}{2} x=\frac{3-\sqrt{21}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x^{2} ni olish uchun 4x^{2} va -2x^{2} ni birlashtirish.

$$2x^{2}+4x+2-10x-8=0$$

-6x ni olish uchun 4x va -10x ni birlashtirish.

$$2x^{2}-6x+2-8=0$$

-6 olish uchun 2 dan 8 ni ayirish.

$$2x^{2}-6x-6=0$$

6 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2x^{2}-6x=6$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-6x}{2}=\frac{6}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{6}{2}\right)x=\frac{6}{2}$$

-6 ni 2 ga bo'lish.

$$x^{2}-3x=\frac{6}{2}$$

6 ni 2 ga bo'lish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

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

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

$$x^{2}-3x+\frac{9}{4}=\frac{21}{4}$$

x^{2}-3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{21}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{21}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{\sqrt{21}}{2} x-\frac{3}{2}=-\frac{\sqrt{21}}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{21}+3}{2} x=\frac{3-\sqrt{21}}{2}$$