x^2-20x-496 eching

$$x ^ { 2 } - 20 x - 496$$

Omil

$$\left(x-\left(10-2\sqrt{149}\right)\right)\left(x-\left(2\sqrt{149}+10\right)\right)$$

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.

$$x^{2}-20x-496=0$$

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.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\left(-496\right)}}{2}$$

-20 kvadratini chiqarish.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\left(-496\right)}}{2}$$

-4 ni -496 marotabaga ko'paytirish.

$$x=\frac{-\left(-20\right)±\sqrt{400+1984}}{2}$$

400 ni 1984 ga qo'shish.

$$x=\frac{-\left(-20\right)±\sqrt{2384}}{2}$$

2384 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-20\right)±4\sqrt{149}}{2}$$

-20 ning teskarisi 20 ga teng.

$$x=\frac{20±4\sqrt{149}}{2}$$

x=\frac{20±4\sqrt{149}}{2} tenglamasini yeching, bunda ± musbat. 20 ni 4\sqrt{149} ga qo'shish.

$$x=\frac{4\sqrt{149}+20}{2}$$

20+4\sqrt{149} ni 2 ga bo'lish.

$$x=2\sqrt{149}+10$$

x=\frac{20±4\sqrt{149}}{2} tenglamasini yeching, bunda ± manfiy. 20 dan 4\sqrt{149} ni ayirish.

$$x=\frac{20-4\sqrt{149}}{2}$$

20-4\sqrt{149} ni 2 ga bo'lish.

$$x=10-2\sqrt{149}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 10+2\sqrt{149} ga va x_{2} uchun 10-2\sqrt{149} ga bo‘ling.

$$x^{2}-20x-496=\left(x-\left(2\sqrt{149}+10\right)\right)\left(x-\left(10-2\sqrt{149}\right)\right)$$

Baholash

$$x^{2}-20x-496$$