11x^2+9-4x-8x^2-15x eching

$$11 x ^ { 2 } + 9 - 4 x - 8 x ^ { 2 } - 15 x$$

Baholash

$$3x^{2}-19x+9$$

Yechim qadamlari

3x^{2} ni olish uchun 11x^{2} va -8x^{2} ni birlashtirish.

$$3x^{2}+9-4x-15x$$

-19x ni olish uchun -4x va -15x ni birlashtirish.

$$3x^{2}+9-19x$$

Omil

$$3\left(x-\frac{19-\sqrt{253}}{6}\right)\left(x-\frac{\sqrt{253}+19}{6}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x^{2} ni olish uchun 11x^{2} va -8x^{2} ni birlashtirish.

$$factor(3x^{2}+9-4x-15x)$$

-19x ni olish uchun -4x va -15x ni birlashtirish.

$$factor(3x^{2}+9-19x)$$

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.

$$3x^{2}-19x+9=0$$

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.

$$x=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 3\times 9}}{2\times 3}$$

-19 kvadratini chiqarish.

$$x=\frac{-\left(-19\right)±\sqrt{361-4\times 3\times 9}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-19\right)±\sqrt{361-12\times 9}}{2\times 3}$$

-12 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-19\right)±\sqrt{361-108}}{2\times 3}$$

361 ni -108 ga qo'shish.

$$x=\frac{-\left(-19\right)±\sqrt{253}}{2\times 3}$$

-19 ning teskarisi 19 ga teng.

$$x=\frac{19±\sqrt{253}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{19±\sqrt{253}}{6}$$

x=\frac{19±\sqrt{253}}{6} tenglamasini yeching, bunda ± musbat. 19 ni \sqrt{253} ga qo'shish.

$$x=\frac{\sqrt{253}+19}{6}$$

x=\frac{19±\sqrt{253}}{6} tenglamasini yeching, bunda ± manfiy. 19 dan \sqrt{253} ni ayirish.

$$x=\frac{19-\sqrt{253}}{6}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{19+\sqrt{253}}{6} ga va x_{2} uchun \frac{19-\sqrt{253}}{6} ga bo‘ling.

$$3x^{2}-19x+9=3\left(x-\frac{\sqrt{253}+19}{6}\right)\left(x-\frac{19-\sqrt{253}}{6}\right)$$