5x+3+1-x^2-x= eching

$$5x+3+1- { x }^{ 2 } -x=$$

Baholash

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

Yechim qadamlari

4 olish uchun 3 va 1'ni qo'shing.

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

4x ni olish uchun 5x va -x ni birlashtirish.

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

Omil

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

Kvadrat tenglamalaridan foydalanish qoidalari

4 olish uchun 3 va 1'ni qo'shing.

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

4x ni olish uchun 5x va -x ni birlashtirish.

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

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.

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

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.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+4\times 4}}{2\left(-1\right)}$$

4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+16}}{2\left(-1\right)}$$

16 ni 16 ga qo'shish.

$$x=\frac{-4±\sqrt{32}}{2\left(-1\right)}$$

32 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4\sqrt{2}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±4\sqrt{2}}{-2}$$

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

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

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

$$x=2-2\sqrt{2}$$

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

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

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

$$x=2\sqrt{2}+2$$

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

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