44=x(x-3)/2 eching

$$44= \frac{ x(x-3) }{ 2 }$$

x uchun yechish

$$x=-8$$

$$x=11$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafini 2 ga ko‘paytiring.

$$44\times 2=x\left(x-3\right)$$

88 hosil qilish uchun 44 va 2 ni ko'paytirish.

$$88=x\left(x-3\right)$$

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

$$88=x^{2}-3x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x=88$$

Ikkala tarafdan 88 ni ayirish.

$$x^{2}-3x-88=0$$

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 -88 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-88\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-88\right)}}{2}$$

-4 ni -88 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+352}}{2}$$

9 ni 352 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{361}}{2}$$

361 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±19}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±19}{2}$$

x=\frac{3±19}{2} tenglamasini yeching, bunda ± musbat. 3 ni 19 ga qo'shish.

$$x=\frac{22}{2}$$

22 ni 2 ga bo'lish.

$$x=11$$

x=\frac{3±19}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 19 ni ayirish.

$$x=-\frac{16}{2}$$

-16 ni 2 ga bo'lish.

$$x=-8$$

Tenglama yechildi.

$$x=11 x=-8$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafini 2 ga ko‘paytiring.

$$44\times 2=x\left(x-3\right)$$

88 hosil qilish uchun 44 va 2 ni ko'paytirish.

$$88=x\left(x-3\right)$$

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

$$88=x^{2}-3x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x=88$$

-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.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=88+\left(-\frac{3}{2}\right)^{2}$$

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

$$x^{2}-3x+\frac{9}{4}=88+\frac{9}{4}$$

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

$$x^{2}-3x+\frac{9}{4}=\frac{361}{4}$$

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.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{361}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{361}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{19}{2} x-\frac{3}{2}=-\frac{19}{2}$$

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

$$x=11 x=-8$$