8x^2+25x eching

$$8 x ^ { 2 } + 25 x$$

Omil

$$x\left(8x+25\right)$$

Yechim qadamlari

x omili.

$$x\left(8x+25\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$8x^{2}+25x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-25±\sqrt{25^{2}}}{2\times 8}$$

25^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-25±25}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{-25±25}{16}$$

x=\frac{-25±25}{16} tenglamasini yeching, bunda ± musbat. -25 ni 25 ga qo'shish.

$$x=\frac{0}{16}$$

0 ni 16 ga bo'lish.

$$x=0$$

x=\frac{-25±25}{16} tenglamasini yeching, bunda ± manfiy. -25 dan 25 ni ayirish.

$$x=-\frac{50}{16}$$

\frac{-50}{16} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{25}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 0 ga va x_{2} uchun -\frac{25}{8} ga bo‘ling.

$$8x^{2}+25x=8x\left(x-\left(-\frac{25}{8}\right)\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$8x^{2}+25x=8x\left(x+\frac{25}{8}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{25}{8} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$8x^{2}+25x=8x\times \frac{8x+25}{8}$$

8 va 8 ichida eng katta umumiy 8 faktorini bekor qiling.

$$8x^{2}+25x=x\left(8x+25\right)$$

Baholash

$$x\left(8x+25\right)$$