(-2x)^2=(x+9)*(x) eching

$$( - 2 x ) ^ { 2 } = ( x + 9 ) \cdot ( x )$$

x uchun yechish

$$x=3$$

$$x=0$$

Faktorlash qadamlari

\left(-2x\right)^{2} ni kengaytirish.

$$\left(-2\right)^{2}x^{2}=\left(x+9\right)x$$

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

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

x+9 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}=x^{2}+9x$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-x^{2}=9x$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}=9x$$

Ikkala tarafdan 9x ni ayirish.

$$3x^{2}-9x=0$$

x omili.

$$x\left(3x-9\right)=0$$

Tenglamani yechish uchun x=0 va 3x-9=0 ni yeching.

$$x=0 x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(-2x\right)^{2} ni kengaytirish.

$$\left(-2\right)^{2}x^{2}=\left(x+9\right)x$$

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

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

x+9 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}=x^{2}+9x$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-x^{2}=9x$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}=9x$$

Ikkala tarafdan 9x ni ayirish.

$$3x^{2}-9x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -9 ni b va 0 ni c bilan almashtiring.

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

\left(-9\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±9}{2\times 3}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±9}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{9±9}{6}$$

x=\frac{9±9}{6} tenglamasini yeching, bunda ± musbat. 9 ni 9 ga qo'shish.

$$x=\frac{18}{6}$$

18 ni 6 ga bo'lish.

$$x=3$$

x=\frac{9±9}{6} tenglamasini yeching, bunda ± manfiy. 9 dan 9 ni ayirish.

$$x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=3 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

\left(-2x\right)^{2} ni kengaytirish.

$$\left(-2\right)^{2}x^{2}=\left(x+9\right)x$$

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

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

x+9 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}=x^{2}+9x$$

Ikkala tarafdan x^{2} ni ayirish.

$$4x^{2}-x^{2}=9x$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}=9x$$

Ikkala tarafdan 9x ni ayirish.

$$3x^{2}-9x=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-9x}{3}=\frac{0}{3}$$

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

$$x^{2}+\left(-\frac{9}{3}\right)x=\frac{0}{3}$$

-9 ni 3 ga bo'lish.

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

0 ni 3 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.

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

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

$$x=3 x=0$$