3x^2-2-8x^2+6+5x eching

$$3 x ^ { 2 } - 2 - 8 x ^ { 2 } + 6 + 5 x$$

Baholash

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

Yechim qadamlari

-5x^{2} ni olish uchun 3x^{2} va -8x^{2} ni birlashtirish.

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

4 olish uchun -2 va 6'ni qo'shing.

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

Omil

$$-5\left(x-\left(-\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-5x^{2} ni olish uchun 3x^{2} va -8x^{2} ni birlashtirish.

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

4 olish uchun -2 va 6'ni qo'shing.

$$factor(-5x^{2}+4+5x)$$

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.

$$-5x^{2}+5x+4=0$$

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.

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

5 kvadratini chiqarish.

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

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+20\times 4}}{2\left(-5\right)}$$

20 ni 4 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+80}}{2\left(-5\right)}$$

25 ni 80 ga qo'shish.

$$x=\frac{-5±\sqrt{105}}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{105}}{-10}$$

x=\frac{-5±\sqrt{105}}{-10} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{105} ga qo'shish.

$$x=\frac{\sqrt{105}-5}{-10}$$

-5+\sqrt{105} ni -10 ga bo'lish.

$$x=-\frac{\sqrt{105}}{10}+\frac{1}{2}$$

x=\frac{-5±\sqrt{105}}{-10} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{105} ni ayirish.

$$x=\frac{-\sqrt{105}-5}{-10}$$

-5-\sqrt{105} ni -10 ga bo'lish.

$$x=\frac{\sqrt{105}}{10}+\frac{1}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1}{2}-\frac{\sqrt{105}}{10} ga va x_{2} uchun \frac{1}{2}+\frac{\sqrt{105}}{10} ga bo‘ling.

$$-5x^{2}+5x+4=-5\left(x-\left(-\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)$$