(x^2+3x-7)+(6x-5) eching

$$( x ^ { 2 } + 3 x - 7 ) + ( 6 x - 5 )$$

Baholash

$$x^{2}+9x-12$$

Yechim qadamlari

9x ni olish uchun 3x va 6x ni birlashtirish.

$$x^{2}+9x-7-5$$

-12 olish uchun -7 dan 5 ni ayirish.

$$x^{2}+9x-12$$

Omil

$$\left(x-\frac{-\sqrt{129}-9}{2}\right)\left(x-\frac{\sqrt{129}-9}{2}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

9x ni olish uchun 3x va 6x ni birlashtirish.

$$factor(x^{2}+9x-7-5)$$

-12 olish uchun -7 dan 5 ni ayirish.

$$factor(x^{2}+9x-12)$$

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.

$$x^{2}+9x-12=0$$

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.

$$x=\frac{-9±\sqrt{9^{2}-4\left(-12\right)}}{2}$$

9 kvadratini chiqarish.

$$x=\frac{-9±\sqrt{81-4\left(-12\right)}}{2}$$

-4 ni -12 marotabaga ko'paytirish.

$$x=\frac{-9±\sqrt{81+48}}{2}$$

81 ni 48 ga qo'shish.

$$x=\frac{-9±\sqrt{129}}{2}$$

x=\frac{-9±\sqrt{129}}{2} tenglamasini yeching, bunda ± musbat. -9 ni \sqrt{129} ga qo'shish.

$$x=\frac{\sqrt{129}-9}{2}$$

x=\frac{-9±\sqrt{129}}{2} tenglamasini yeching, bunda ± manfiy. -9 dan \sqrt{129} ni ayirish.

$$x=\frac{-\sqrt{129}-9}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-9+\sqrt{129}}{2} ga va x_{2} uchun \frac{-9-\sqrt{129}}{2} ga bo‘ling.

$$x^{2}+9x-12=\left(x-\frac{\sqrt{129}-9}{2}\right)\left(x-\frac{-\sqrt{129}-9}{2}\right)$$