(x+3)(x-2)=24 eching

$$( x + 3 ) ( x - 2 ) = 24$$

x uchun yechish

$$x=-6$$

$$x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+3 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+x-6=24$$

Ikkala tarafdan 24 ni ayirish.

$$x^{2}+x-6-24=0$$

-30 olish uchun -6 dan 24 ni ayirish.

$$x^{2}+x-30=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 1 ni b va -30 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-30\right)}}{2}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-30\right)}}{2}$$

-4 ni -30 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+120}}{2}$$

1 ni 120 ga qo'shish.

$$x=\frac{-1±\sqrt{121}}{2}$$

121 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±11}{2}$$

x=\frac{-1±11}{2} tenglamasini yeching, bunda ± musbat. -1 ni 11 ga qo'shish.

$$x=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$x=5$$

x=\frac{-1±11}{2} tenglamasini yeching, bunda ± manfiy. -1 dan 11 ni ayirish.

$$x=-\frac{12}{2}$$

-12 ni 2 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=5 x=-6$$

Kvadratni yakunlash bo'yicha qadamlar

x+3 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+x-6=24$$

6 ni ikki tarafga qo’shing.

$$x^{2}+x=24+6$$

30 olish uchun 24 va 6'ni qo'shing.

$$x^{2}+x=30$$

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

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=30+\left(\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{2} kvadratini chiqarish.

$$x^{2}+x+\frac{1}{4}=30+\frac{1}{4}$$

30 ni \frac{1}{4} ga qo'shish.

$$x^{2}+x+\frac{1}{4}=\frac{121}{4}$$

x^{2}+x+\frac{1}{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.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{121}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Qisqartirish.

$$x+\frac{1}{2}=\frac{11}{2} x+\frac{1}{2}=-\frac{11}{2}$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$x=5 x=-6$$