14x-x^2-4 eching

$$14 x - x ^ { 2 } - 4$$

Omil

$$-\left(x-\left(7-3\sqrt{5}\right)\right)\left(x-\left(3\sqrt{5}+7\right)\right)$$

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.

$$-x^{2}+14x-4=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-1\right)\left(-4\right)}}{2\left(-1\right)}$$

14 kvadratini chiqarish.

$$x=\frac{-14±\sqrt{196-4\left(-1\right)\left(-4\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+4\left(-4\right)}}{2\left(-1\right)}$$

4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196-16}}{2\left(-1\right)}$$

196 ni -16 ga qo'shish.

$$x=\frac{-14±\sqrt{180}}{2\left(-1\right)}$$

180 ning kvadrat ildizini chiqarish.

$$x=\frac{-14±6\sqrt{5}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-14±6\sqrt{5}}{-2}$$

x=\frac{-14±6\sqrt{5}}{-2} tenglamasini yeching, bunda ± musbat. -14 ni 6\sqrt{5} ga qo'shish.

$$x=\frac{6\sqrt{5}-14}{-2}$$

-14+6\sqrt{5} ni -2 ga bo'lish.

$$x=7-3\sqrt{5}$$

x=\frac{-14±6\sqrt{5}}{-2} tenglamasini yeching, bunda ± manfiy. -14 dan 6\sqrt{5} ni ayirish.

$$x=\frac{-6\sqrt{5}-14}{-2}$$

-14-6\sqrt{5} ni -2 ga bo'lish.

$$x=3\sqrt{5}+7$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 7-3\sqrt{5} ga va x_{2} uchun 7+3\sqrt{5} ga bo‘ling.

$$-x^{2}+14x-4=-\left(x-\left(7-3\sqrt{5}\right)\right)\left(x-\left(3\sqrt{5}+7\right)\right)$$

Baholash

$$-x^{2}+14x-4$$