-1-5x-2x^2 eching

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

Omil

$$-2\left(x-\frac{-\sqrt{17}-5}{4}\right)\left(x-\frac{\sqrt{17}-5}{4}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

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

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.

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

-5 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25+8\left(-1\right)}}{2\left(-2\right)}$$

8 ni -1 marotabaga ko'paytirish.

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

25 ni -8 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{17}}{2\left(-2\right)}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±\sqrt{17}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{5±\sqrt{17}}{-4}$$

x=\frac{5±\sqrt{17}}{-4} tenglamasini yeching, bunda ± musbat. 5 ni \sqrt{17} ga qo'shish.

$$x=\frac{\sqrt{17}+5}{-4}$$

5+\sqrt{17} ni -4 ga bo'lish.

$$x=\frac{-\sqrt{17}-5}{4}$$

x=\frac{5±\sqrt{17}}{-4} tenglamasini yeching, bunda ± manfiy. 5 dan \sqrt{17} ni ayirish.

$$x=\frac{5-\sqrt{17}}{-4}$$

5-\sqrt{17} ni -4 ga bo'lish.

$$x=\frac{\sqrt{17}-5}{4}$$

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{17}}{4} ga va x_{2} uchun \frac{-5+\sqrt{17}}{4} ga bo‘ling.

$$-2x^{2}-5x-1=-2\left(x-\frac{-\sqrt{17}-5}{4}\right)\left(x-\frac{\sqrt{17}-5}{4}\right)$$

Baholash

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