-16x^2-128x+48 eching

$$- 16 x ^ { 2 } - 128 x + 48$$

Omil

$$-16\left(x-\left(-\sqrt{19}-4\right)\right)\left(x-\left(\sqrt{19}-4\right)\right)$$

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.

$$-16x^{2}-128x+48=0$$

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.

$$x=\frac{-\left(-128\right)±\sqrt{\left(-128\right)^{2}-4\left(-16\right)\times 48}}{2\left(-16\right)}$$

-128 kvadratini chiqarish.

$$x=\frac{-\left(-128\right)±\sqrt{16384-4\left(-16\right)\times 48}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$x=\frac{-\left(-128\right)±\sqrt{16384+64\times 48}}{2\left(-16\right)}$$

64 ni 48 marotabaga ko'paytirish.

$$x=\frac{-\left(-128\right)±\sqrt{16384+3072}}{2\left(-16\right)}$$

16384 ni 3072 ga qo'shish.

$$x=\frac{-\left(-128\right)±\sqrt{19456}}{2\left(-16\right)}$$

19456 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-128\right)±32\sqrt{19}}{2\left(-16\right)}$$

-128 ning teskarisi 128 ga teng.

$$x=\frac{128±32\sqrt{19}}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$x=\frac{128±32\sqrt{19}}{-32}$$

x=\frac{128±32\sqrt{19}}{-32} tenglamasini yeching, bunda ± musbat. 128 ni 32\sqrt{19} ga qo'shish.

$$x=\frac{32\sqrt{19}+128}{-32}$$

128+32\sqrt{19} ni -32 ga bo'lish.

$$x=-\left(\sqrt{19}+4\right)$$

x=\frac{128±32\sqrt{19}}{-32} tenglamasini yeching, bunda ± manfiy. 128 dan 32\sqrt{19} ni ayirish.

$$x=\frac{128-32\sqrt{19}}{-32}$$

128-32\sqrt{19} ni -32 ga bo'lish.

$$x=\sqrt{19}-4$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\left(4+\sqrt{19}\right) ga va x_{2} uchun -4+\sqrt{19} ga bo‘ling.

$$-16x^{2}-128x+48=-16\left(x-\left(-\left(\sqrt{19}+4\right)\right)\right)\left(x-\left(\sqrt{19}-4\right)\right)$$

Baholash

$$48-128x-16x^{2}$$