x*(x+5)=150 eching

$$x \times (x+5)=150$$

x uchun yechish

$$x=-15$$

$$x=10$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}+5x=150$$

Ikkala tarafdan 150 ni ayirish.

$$x^{2}+5x-150=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 5 ni b va -150 ni c bilan almashtiring.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-150\right)}}{2}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\left(-150\right)}}{2}$$

-4 ni -150 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+600}}{2}$$

25 ni 600 ga qo'shish.

$$x=\frac{-5±\sqrt{625}}{2}$$

625 ning kvadrat ildizini chiqarish.

$$x=\frac{-5±25}{2}$$

x=\frac{-5±25}{2} tenglamasini yeching, bunda ± musbat. -5 ni 25 ga qo'shish.

$$x=\frac{20}{2}$$

20 ni 2 ga bo'lish.

$$x=10$$

x=\frac{-5±25}{2} tenglamasini yeching, bunda ± manfiy. -5 dan 25 ni ayirish.

$$x=-\frac{30}{2}$$

-30 ni 2 ga bo'lish.

$$x=-15$$

Tenglama yechildi.

$$x=10 x=-15$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}+5x=150$$

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.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=150+\left(\frac{5}{2}\right)^{2}$$

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

$$x^{2}+5x+\frac{25}{4}=150+\frac{25}{4}$$

150 ni \frac{25}{4} ga qo'shish.

$$x^{2}+5x+\frac{25}{4}=\frac{625}{4}$$

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.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{625}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{625}{4}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{5}{2} ni ayirish.

$$x=10 x=-15$$