4x^2=-8x eching

$$4 { x }^{ 2 } =-8x$$

x uchun yechish

$$x=-2$$

$$x=0$$

Faktorlash qadamlari

8x ni ikki tarafga qo’shing.

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

x omili.

$$x\left(4x+8\right)=0$$

Tenglamani yechish uchun x=0 va 4x+8=0 ni yeching.

$$x=0 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

8x ni ikki tarafga qo’shing.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 8 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}}}{2\times 4}$$

8^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-8±8}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-8±8}{8}$$

x=\frac{-8±8}{8} tenglamasini yeching, bunda ± musbat. -8 ni 8 ga qo'shish.

$$x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x=0$$

x=\frac{-8±8}{8} tenglamasini yeching, bunda ± manfiy. -8 dan 8 ni ayirish.

$$x=-\frac{16}{8}$$

-16 ni 8 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=0 x=-2$$

Kvadratni yakunlash bo'yicha qadamlar

8x ni ikki tarafga qo’shing.

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

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}+8x}{4}=\frac{0}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{8}{4}x=\frac{0}{4}$$

8 ni 4 ga bo'lish.

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

0 ni 4 ga bo'lish.

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

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

$$x^{2}+2x+1^{2}=1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=1$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$x+1=1 x+1=-1$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=0 x=-2$$