2x^2-8x-2x=0 eching

$$2 x ^ { 2 } - 8 x - 2 x = 0$$

x uchun yechish

$$x=5$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(2x-8-2\right)=0$$

Tenglamani yechish uchun x=0 va 2x-10=0 ni yeching.

$$x=0 x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

-10x ni olish uchun -8x va -2x ni birlashtirish.

$$2x^{2}-10x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -10 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 2}$$

\left(-10\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-10\right)±10}{2\times 2}$$

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±10}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{10±10}{4}$$

x=\frac{10±10}{4} tenglamasini yeching, bunda ± musbat. 10 ni 10 ga qo'shish.

$$x=\frac{20}{4}$$

20 ni 4 ga bo'lish.

$$x=5$$

x=\frac{10±10}{4} tenglamasini yeching, bunda ± manfiy. 10 dan 10 ni ayirish.

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

0 ni 4 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=5 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

-10x ni olish uchun -8x va -2x ni birlashtirish.

$$2x^{2}-10x=0$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-10x}{2}=\frac{0}{2}$$

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

$$x^{2}+\left(-\frac{10}{2}\right)x=\frac{0}{2}$$

-10 ni 2 ga bo'lish.

$$x^{2}-5x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x^{2}-5x=0$$

-5 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{2} olish uchun. Keyin, -\frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=\left(-\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$x^{2}-5x+\frac{25}{4}=\frac{25}{4}$$

x^{2}-5x+\frac{25}{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.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

$$x-\frac{5}{2}=\frac{5}{2} x-\frac{5}{2}=-\frac{5}{2}$$

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=5 x=0$$