(x-9)(x+4)=20 eching

$$( x - 9 ) ( x + 4 ) = 20$$

x uchun yechish

$$x = \frac{\sqrt{249} + 5}{2} \approx 10,389866919$$

$$x=\frac{5-\sqrt{249}}{2}\approx -5,389866919$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-9 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-5x-36=20$$

Ikkala tarafdan 20 ni ayirish.

$$x^{2}-5x-36-20=0$$

-56 olish uchun -36 dan 20 ni ayirish.

$$x^{2}-5x-56=0$$

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 -56 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-56\right)}}{2}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-56\right)}}{2}$$

-4 ni -56 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25+224}}{2}$$

25 ni 224 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{249}}{2}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±\sqrt{249}}{2}$$

x=\frac{5±\sqrt{249}}{2} tenglamasini yeching, bunda ± musbat. 5 ni \sqrt{249} ga qo'shish.

$$x=\frac{\sqrt{249}+5}{2}$$

x=\frac{5±\sqrt{249}}{2} tenglamasini yeching, bunda ± manfiy. 5 dan \sqrt{249} ni ayirish.

$$x=\frac{5-\sqrt{249}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{249}+5}{2} x=\frac{5-\sqrt{249}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x-9 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-5x-36=20$$

36 ni ikki tarafga qo’shing.

$$x^{2}-5x=20+36$$

56 olish uchun 20 va 36'ni qo'shing.

$$x^{2}-5x=56$$

-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.

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=56+\left(-\frac{5}{2}\right)^{2}$$

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

$$x^{2}-5x+\frac{25}{4}=56+\frac{25}{4}$$

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

$$x^{2}-5x+\frac{25}{4}=\frac{249}{4}$$

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.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{249}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{249}{4}}$$

Qisqartirish.

$$x-\frac{5}{2}=\frac{\sqrt{249}}{2} x-\frac{5}{2}=-\frac{\sqrt{249}}{2}$$

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

$$x=\frac{\sqrt{249}+5}{2} x=\frac{5-\sqrt{249}}{2}$$