x^2+3x-4x^2-5x+6x^2-2x-3 eching

$$x ^ { 2 } + 3 x - 4 x ^ { 2 } - 5 x + 6 x ^ { 2 } - 2 x - 3$$

Baholash

$$3x^{2}-4x-3$$

Yechim qadamlari

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$-3x^{2}+3x-5x+6x^{2}-2x-3$$

-2x ni olish uchun 3x va -5x ni birlashtirish.

$$-3x^{2}-2x+6x^{2}-2x-3$$

3x^{2} ni olish uchun -3x^{2} va 6x^{2} ni birlashtirish.

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

-4x ni olish uchun -2x va -2x ni birlashtirish.

$$3x^{2}-4x-3$$

Omil

$$3\left(x-\frac{2-\sqrt{13}}{3}\right)\left(x-\frac{\sqrt{13}+2}{3}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-3x^{2} ni olish uchun x^{2} va -4x^{2} ni birlashtirish.

$$factor(-3x^{2}+3x-5x+6x^{2}-2x-3)$$

-2x ni olish uchun 3x va -5x ni birlashtirish.

$$factor(-3x^{2}-2x+6x^{2}-2x-3)$$

3x^{2} ni olish uchun -3x^{2} va 6x^{2} ni birlashtirish.

$$factor(3x^{2}-2x-2x-3)$$

-4x ni olish uchun -2x va -2x ni birlashtirish.

$$factor(3x^{2}-4x-3)$$

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.

$$3x^{2}-4x-3=0$$

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.

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

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 3\left(-3\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-12\left(-3\right)}}{2\times 3}$$

-12 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+36}}{2\times 3}$$

16 ni 36 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{52}}{2\times 3}$$

52 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{13}}{2\times 3}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{13}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{4±2\sqrt{13}}{6}$$

x=\frac{4±2\sqrt{13}}{6} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{13} ga qo'shish.

$$x=\frac{2\sqrt{13}+4}{6}$$

4+2\sqrt{13} ni 6 ga bo'lish.

$$x=\frac{\sqrt{13}+2}{3}$$

x=\frac{4±2\sqrt{13}}{6} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{13} ni ayirish.

$$x=\frac{4-2\sqrt{13}}{6}$$

4-2\sqrt{13} ni 6 ga bo'lish.

$$x=\frac{2-\sqrt{13}}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{2+\sqrt{13}}{3} ga va x_{2} uchun \frac{2-\sqrt{13}}{3} ga bo‘ling.

$$3x^{2}-4x-3=3\left(x-\frac{\sqrt{13}+2}{3}\right)\left(x-\frac{2-\sqrt{13}}{3}\right)$$