x^2-10x+15-3(5-x)=0 eching

$${ x }^{ 2 } -10x+15-3(5-x)=0$$

x uchun yechish

$$x=7$$

$$x=0$$

Faktorlash qadamlari

-3 ga 5-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-10x+15-15+3x=0$$

0 olish uchun 15 dan 15 ni ayirish.

$$x^{2}-10x+3x=0$$

-7x ni olish uchun -10x va 3x ni birlashtirish.

$$x^{2}-7x=0$$

x omili.

$$x\left(x-7\right)=0$$

Tenglamani yechish uchun x=0 va x-7=0 ni yeching.

$$x=0 x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

-3 ga 5-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-10x+15-15+3x=0$$

0 olish uchun 15 dan 15 ni ayirish.

$$x^{2}-10x+3x=0$$

-7x ni olish uchun -10x va 3x ni birlashtirish.

$$x^{2}-7x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -7 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2}$$

\left(-7\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-7\right)±7}{2}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±7}{2}$$

x=\frac{7±7}{2} tenglamasini yeching, bunda ± musbat. 7 ni 7 ga qo'shish.

$$x=\frac{14}{2}$$

14 ni 2 ga bo'lish.

$$x=7$$

x=\frac{7±7}{2} tenglamasini yeching, bunda ± manfiy. 7 dan 7 ni ayirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=7 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

-3 ga 5-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-10x+15-15+3x=0$$

0 olish uchun 15 dan 15 ni ayirish.

$$x^{2}-10x+3x=0$$

-7x ni olish uchun -10x va 3x ni birlashtirish.

$$x^{2}-7x=0$$

-7 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{2} olish uchun. Keyin, -\frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

x^{2}-7x+\frac{49}{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.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=0$$