2x^2+4x+2x=0 eching

$$2 { x }^{ 2 } +4x+2x=0$$

x uchun yechish

$$x=-3$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(2x+4+2\right)=0$$

Tenglamani yechish uchun x=0 va 2x+6=0 ni yeching.

$$x=0 x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

6x ni olish uchun 4x va 2x ni birlashtirish.

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

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 0 ni c bilan almashtiring.

$$x=\frac{-6±\sqrt{6^{2}}}{2\times 2}$$

6^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-6±6}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-6±6}{4}$$

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

$$x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x=0$$

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

$$x=-\frac{12}{4}$$

-12 ni 4 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=0 x=-3$$

Kvadratni yakunlash bo'yicha qadamlar

6x ni olish uchun 4x va 2x ni birlashtirish.

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

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+6x}{2}=\frac{0}{2}$$

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

$$x^{2}+\frac{6}{2}x=\frac{0}{2}$$

6 ni 2 ga bo'lish.

$$x^{2}+3x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x^{2}+3x=0$$

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.

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

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

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

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.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$x=0 x=-3$$