-9x^2-15x eching

$$- 9 x ^ { 2 } - 15 x$$

Omil

$$-3x\left(3x+5\right)$$

Yechim qadamlari

3 omili.

$$3\left(-3x^{2}-5x\right)$$

Hisoblang: -3x^{2}-5x. x omili.

$$x\left(-3x-5\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$3x\left(-3x-5\right)$$

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.

$$-9x^{2}-15x=0$$

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.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2\left(-9\right)}$$

\left(-15\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-15\right)±15}{2\left(-9\right)}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±15}{2\left(-9\right)}$$

2 ni -9 marotabaga ko'paytirish.

$$x=\frac{15±15}{-18}$$

x=\frac{15±15}{-18} tenglamasini yeching, bunda ± musbat. 15 ni 15 ga qo'shish.

$$x=\frac{30}{-18}$$

\frac{30}{-18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{5}{3}$$

x=\frac{15±15}{-18} tenglamasini yeching, bunda ± manfiy. 15 dan 15 ni ayirish.

$$x=\frac{0}{-18}$$

0 ni -18 ga bo'lish.

$$x=0$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{5}{3} ga va x_{2} uchun 0 ga bo‘ling.

$$-9x^{2}-15x=-9\left(x-\left(-\frac{5}{3}\right)\right)x$$

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

$$-9x^{2}-15x=-9\left(x+\frac{5}{3}\right)x$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5}{3} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$-9x^{2}-15x=-9\times \frac{-3x-5}{-3}x$$

-9 va -3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$-9x^{2}-15x=3\left(-3x-5\right)x$$

Baholash

$$-3x\left(3x+5\right)$$