x*(2x-9)=35 eching

$$x \times (2x-9)=35$$

x uchun yechish

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2,5$$

$$x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga 2x-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}-9x=35$$

Ikkala tarafdan 35 ni ayirish.

$$2x^{2}-9x-35=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -9 ni b va -35 ni c bilan almashtiring.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 2\left(-35\right)}}{2\times 2}$$

-9 kvadratini chiqarish.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 2\left(-35\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81-8\left(-35\right)}}{2\times 2}$$

-8 ni -35 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81+280}}{2\times 2}$$

81 ni 280 ga qo'shish.

$$x=\frac{-\left(-9\right)±\sqrt{361}}{2\times 2}$$

361 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±19}{2\times 2}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±19}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{9±19}{4}$$

x=\frac{9±19}{4} tenglamasini yeching, bunda ± musbat. 9 ni 19 ga qo'shish.

$$x=\frac{28}{4}$$

28 ni 4 ga bo'lish.

$$x=7$$

x=\frac{9±19}{4} tenglamasini yeching, bunda ± manfiy. 9 dan 19 ni ayirish.

$$x=-\frac{10}{4}$$

\frac{-10}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

$$x=7 x=-\frac{5}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x ga 2x-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}-9x=35$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-9x}{2}=\frac{35}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{9}{2}x=\frac{35}{2}$$

-\frac{9}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{4} olish uchun. Keyin, -\frac{9}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{9}{2}x+\left(-\frac{9}{4}\right)^{2}=\frac{35}{2}+\left(-\frac{9}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{4} kvadratini chiqarish.

$$x^{2}-\frac{9}{2}x+\frac{81}{16}=\frac{35}{2}+\frac{81}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{35}{2} ni \frac{81}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{9}{2}x+\frac{81}{16}=\frac{361}{16}$$

x^{2}-\frac{9}{2}x+\frac{81}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{9}{4}\right)^{2}=\frac{361}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{4}\right)^{2}}=\sqrt{\frac{361}{16}}$$

Qisqartirish.

$$x-\frac{9}{4}=\frac{19}{4} x-\frac{9}{4}=-\frac{19}{4}$$

\frac{9}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=-\frac{5}{2}$$