(2x+1*3x+1)-x^2 eching

$$(2x+1 \times 3x+1)- { x }^{ 2 }$$

Baholash

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

Yechim qadamlari

3 hosil qilish uchun 1 va 3 ni ko'paytirish.

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

5x ni olish uchun 2x va 3x ni birlashtirish.

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

Omil

$$-\left(x-\frac{5-\sqrt{29}}{2}\right)\left(x-\frac{\sqrt{29}+5}{2}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

3 hosil qilish uchun 1 va 3 ni ko'paytirish.

$$factor(2x+3x+1-x^{2})$$

5x ni olish uchun 2x va 3x ni birlashtirish.

$$factor(5x+1-x^{2})$$

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.

$$-x^{2}+5x+1=0$$

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.

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

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\left(-1\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+4}}{2\left(-1\right)}$$

25 ni 4 ga qo'shish.

$$x=\frac{-5±\sqrt{29}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{29}}{-2}$$

x=\frac{-5±\sqrt{29}}{-2} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{29} ga qo'shish.

$$x=\frac{\sqrt{29}-5}{-2}$$

-5+\sqrt{29} ni -2 ga bo'lish.

$$x=\frac{5-\sqrt{29}}{2}$$

x=\frac{-5±\sqrt{29}}{-2} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{29} ni ayirish.

$$x=\frac{-\sqrt{29}-5}{-2}$$

-5-\sqrt{29} ni -2 ga bo'lish.

$$x=\frac{\sqrt{29}+5}{2}$$

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{29}}{2} ga va x_{2} uchun \frac{5+\sqrt{29}}{2} ga bo‘ling.

$$-x^{2}+5x+1=-\left(x-\frac{5-\sqrt{29}}{2}\right)\left(x-\frac{\sqrt{29}+5}{2}\right)$$