4x^2-20x-5 eching

$$4 x ^ { 2 } - 20 x - 5$$

Omil

$$4\left(x-\frac{5-\sqrt{30}}{2}\right)\left(x-\frac{\sqrt{30}+5}{2}\right)$$

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.

$$4x^{2}-20x-5=0$$

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.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 4\left(-5\right)}}{2\times 4}$$

-20 kvadratini chiqarish.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 4\left(-5\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-20\right)±\sqrt{400-16\left(-5\right)}}{2\times 4}$$

-16 ni -5 marotabaga ko'paytirish.

$$x=\frac{-\left(-20\right)±\sqrt{400+80}}{2\times 4}$$

400 ni 80 ga qo'shish.

$$x=\frac{-\left(-20\right)±\sqrt{480}}{2\times 4}$$

480 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-20\right)±4\sqrt{30}}{2\times 4}$$

-20 ning teskarisi 20 ga teng.

$$x=\frac{20±4\sqrt{30}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{20±4\sqrt{30}}{8}$$

x=\frac{20±4\sqrt{30}}{8} tenglamasini yeching, bunda ± musbat. 20 ni 4\sqrt{30} ga qo'shish.

$$x=\frac{4\sqrt{30}+20}{8}$$

20+4\sqrt{30} ni 8 ga bo'lish.

$$x=\frac{\sqrt{30}+5}{2}$$

x=\frac{20±4\sqrt{30}}{8} tenglamasini yeching, bunda ± manfiy. 20 dan 4\sqrt{30} ni ayirish.

$$x=\frac{20-4\sqrt{30}}{8}$$

20-4\sqrt{30} ni 8 ga bo'lish.

$$x=\frac{5-\sqrt{30}}{2}$$

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{30}}{2} ga va x_{2} uchun \frac{5-\sqrt{30}}{2} ga bo‘ling.

$$4x^{2}-20x-5=4\left(x-\frac{\sqrt{30}+5}{2}\right)\left(x-\frac{5-\sqrt{30}}{2}\right)$$

Baholash

$$4x^{2}-20x-5$$