5x^2+2x=1x^2+3x eching

$$5 x ^ { 2 } + 2 x = 1 x ^ { 2 } + 3 x$$

x uchun yechish

$$x=\frac{1}{4}=0,25$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 1x^{2} ni ayirish.

$$5x^{2}+2x-x^{2}=3x$$

4x^{2} ni olish uchun 5x^{2} va -x^{2} ni birlashtirish.

$$4x^{2}+2x=3x$$

Ikkala tarafdan 3x ni ayirish.

$$4x^{2}+2x-3x=0$$

-x ni olish uchun 2x va -3x ni birlashtirish.

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

x omili.

$$x\left(4x-1\right)=0$$

Tenglamani yechish uchun x=0 va 4x-1=0 ni yeching.

$$x=0 x=\frac{1}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1x^{2} ni ayirish.

$$5x^{2}+2x-x^{2}=3x$$

4x^{2} ni olish uchun 5x^{2} va -x^{2} ni birlashtirish.

$$4x^{2}+2x=3x$$

Ikkala tarafdan 3x ni ayirish.

$$4x^{2}+2x-3x=0$$

-x ni olish uchun 2x va -3x ni birlashtirish.

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

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

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 4}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±1}{2\times 4}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±1}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{1±1}{8}$$

x=\frac{1±1}{8} tenglamasini yeching, bunda ± musbat. 1 ni 1 ga qo'shish.

$$x=\frac{2}{8}$$

\frac{2}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{4}$$

x=\frac{1±1}{8} tenglamasini yeching, bunda ± manfiy. 1 dan 1 ni ayirish.

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

0 ni 8 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{1}{4} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 1x^{2} ni ayirish.

$$5x^{2}+2x-x^{2}=3x$$

4x^{2} ni olish uchun 5x^{2} va -x^{2} ni birlashtirish.

$$4x^{2}+2x=3x$$

Ikkala tarafdan 3x ni ayirish.

$$4x^{2}+2x-3x=0$$

-x ni olish uchun 2x va -3x ni birlashtirish.

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

Ikki tarafini 4 ga bo‘ling.

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

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

$$x^{2}-\frac{1}{4}x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x^{2}-\frac{1}{4}x=0$$

-\frac{1}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{8} olish uchun. Keyin, -\frac{1}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{4}x+\left(-\frac{1}{8}\right)^{2}=\left(-\frac{1}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{8} kvadratini chiqarish.

$$x^{2}-\frac{1}{4}x+\frac{1}{64}=\frac{1}{64}$$

x^{2}-\frac{1}{4}x+\frac{1}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{8}\right)^{2}=\frac{1}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{8}\right)^{2}}=\sqrt{\frac{1}{64}}$$

Qisqartirish.

$$x-\frac{1}{8}=\frac{1}{8} x-\frac{1}{8}=-\frac{1}{8}$$

\frac{1}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1}{4} x=0$$