2x*4x+5x-6 eching

$$2x \times 4x+5x-6$$

Baholash

$$8x^{2}+5x-6$$

Yechim qadamlari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$2x^{2}\times 4+5x-6$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$8x^{2}+5x-6$$

Omil

$$8\left(x-\frac{-\sqrt{217}-5}{16}\right)\left(x-\frac{\sqrt{217}-5}{16}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$factor(2x^{2}\times 4+5x-6)$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$factor(8x^{2}+5x-6)$$

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.

$$8x^{2}+5x-6=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\times 8\left(-6\right)}}{2\times 8}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\times 8\left(-6\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25-32\left(-6\right)}}{2\times 8}$$

-32 ni -6 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+192}}{2\times 8}$$

25 ni 192 ga qo'shish.

$$x=\frac{-5±\sqrt{217}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{217}}{16}$$

x=\frac{-5±\sqrt{217}}{16} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{217} ga qo'shish.

$$x=\frac{\sqrt{217}-5}{16}$$

x=\frac{-5±\sqrt{217}}{16} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{217} ni ayirish.

$$x=\frac{-\sqrt{217}-5}{16}$$

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{217}}{16} ga va x_{2} uchun \frac{-5-\sqrt{217}}{16} ga bo‘ling.

$$8x^{2}+5x-6=8\left(x-\frac{\sqrt{217}-5}{16}\right)\left(x-\frac{-\sqrt{217}-5}{16}\right)$$