1/2x^2=x eching

$$\frac{ 1 }{ 2 } { x }^{ 2 } = x$$

x uchun yechish

$$x=2$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan x ni ayirish.

$$\frac{1}{2}x^{2}-x=0$$

x omili.

$$x\left(\frac{1}{2}x-1\right)=0$$

Tenglamani yechish uchun x=0 va \frac{x}{2}-1=0 ni yeching.

$$x=0 x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x ni ayirish.

$$\frac{1}{2}x^{2}-x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{2} ni a, -1 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times \frac{1}{2}}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±1}{2\times \frac{1}{2}}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±1}{2\times \frac{1}{2}}$$

2 ni \frac{1}{2} marotabaga ko'paytirish.

$$x=\frac{1±1}{1}$$

x=\frac{1±1}{1} tenglamasini yeching, bunda ± musbat. 1 ni 1 ga qo'shish.

$$x=\frac{2}{1}$$

2 ni 1 ga bo'lish.

$$x=2$$

x=\frac{1±1}{1} tenglamasini yeching, bunda ± manfiy. 1 dan 1 ni ayirish.

$$x=\frac{0}{1}$$

0 ni 1 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=2 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x ni ayirish.

$$\frac{1}{2}x^{2}-x=0$$

Ikkala tarafini 2 ga ko‘paytiring.

$$\frac{\frac{1}{2}x^{2}-x}{\frac{1}{2}}=\frac{0}{\frac{1}{2}}$$

\frac{1}{2} ga bo'lish \frac{1}{2} ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{1}{\frac{1}{2}}\right)x=\frac{0}{\frac{1}{2}}$$

-1 ni \frac{1}{2} ga bo'lish -1 ga k'paytirish \frac{1}{2} ga qaytarish.

$$x^{2}-2x=\frac{0}{\frac{1}{2}}$$

0 ni \frac{1}{2} ga bo'lish 0 ga k'paytirish \frac{1}{2} ga qaytarish.

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

-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.

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

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.

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

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2 x=0$$