18=x(x-3) eching

$$18=x(x-3)$$

x uchun yechish

$$x=-3$$

$$x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$18=x^{2}-3x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x=18$$

Ikkala tarafdan 18 ni ayirish.

$$x^{2}-3x-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va -18 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-18\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-18\right)}}{2}$$

-4 ni -18 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+72}}{2}$$

9 ni 72 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{81}}{2}$$

81 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±9}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±9}{2}$$

x=\frac{3±9}{2} tenglamasini yeching, bunda ± musbat. 3 ni 9 ga qo'shish.

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

12 ni 2 ga bo'lish.

$$x=6$$

x=\frac{3±9}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 9 ni ayirish.

$$x=-\frac{6}{2}$$

-6 ni 2 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=6 x=-3$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$18=x^{2}-3x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x=18$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=18+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=18+\frac{9}{4}$$

18 ni \frac{9}{4} ga qo'shish.

$$x^{2}-3x+\frac{9}{4}=\frac{81}{4}$$

x^{2}-3x+\frac{9}{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.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{81}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{9}{2} x-\frac{3}{2}=-\frac{9}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=6 x=-3$$