4a^2+7a eching

$$4 a ^ { 2 } + 7 a$$

Omil

$$a\left(4a+7\right)$$

Yechim qadamlari

a omili.

$$a\left(4a+7\right)$$

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.

$$4a^{2}+7a=0$$

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.

$$a=\frac{-7±\sqrt{7^{2}}}{2\times 4}$$

7^{2} ning kvadrat ildizini chiqarish.

$$a=\frac{-7±7}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$a=\frac{-7±7}{8}$$

a=\frac{-7±7}{8} tenglamasini yeching, bunda ± musbat. -7 ni 7 ga qo'shish.

$$a=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$a=0$$

a=\frac{-7±7}{8} tenglamasini yeching, bunda ± manfiy. -7 dan 7 ni ayirish.

$$a=-\frac{14}{8}$$

\frac{-14}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$a=-\frac{7}{4}$$

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{7}{4} ga bo‘ling.

$$4a^{2}+7a=4a\left(a-\left(-\frac{7}{4}\right)\right)$$

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

$$4a^{2}+7a=4a\left(a+\frac{7}{4}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{7}{4} ni a ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$4a^{2}+7a=4a\times \frac{4a+7}{4}$$

4 va 4 ichida eng katta umumiy 4 faktorini bekor qiling.

$$4a^{2}+7a=a\left(4a+7\right)$$

Baholash

$$a\left(4a+7\right)$$