8x-94-x^2-3x+3x^2+27 eching

$$8 x - 94 - x ^ { 2 } - 3 x + 3 x ^ { 2 } + 27$$

Baholash

$$2x^{2}+5x-67$$

Yechim qadamlari

5x ni olish uchun 8x va -3x ni birlashtirish.

$$5x-94-x^{2}+3x^{2}+27$$

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

$$5x-94+2x^{2}+27$$

-67 olish uchun -94 va 27'ni qo'shing.

$$5x-67+2x^{2}$$

Omil

$$2\left(x-\frac{-\sqrt{561}-5}{4}\right)\left(x-\frac{\sqrt{561}-5}{4}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

5x ni olish uchun 8x va -3x ni birlashtirish.

$$factor(5x-94-x^{2}+3x^{2}+27)$$

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

$$factor(5x-94+2x^{2}+27)$$

-67 olish uchun -94 va 27'ni qo'shing.

$$factor(5x-67+2x^{2})$$

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.

$$2x^{2}+5x-67=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\times 2\left(-67\right)}}{2\times 2}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\times 2\left(-67\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25-8\left(-67\right)}}{2\times 2}$$

-8 ni -67 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+536}}{2\times 2}$$

25 ni 536 ga qo'shish.

$$x=\frac{-5±\sqrt{561}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{561}}{4}$$

x=\frac{-5±\sqrt{561}}{4} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{561} ga qo'shish.

$$x=\frac{\sqrt{561}-5}{4}$$

x=\frac{-5±\sqrt{561}}{4} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{561} ni ayirish.

$$x=\frac{-\sqrt{561}-5}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-5+\sqrt{561}}{4} ga va x_{2} uchun \frac{-5-\sqrt{561}}{4} ga bo‘ling.

$$2x^{2}+5x-67=2\left(x-\frac{\sqrt{561}-5}{4}\right)\left(x-\frac{-\sqrt{561}-5}{4}\right)$$