32x^2-56x+20x-35+15x^2-40 eching

$$32 x ^ { 2 } - 56 x + 20 x - 35 + 15 x ^ { 2 } - 40$$

Baholash

$$47x^{2}-36x-75$$

Yechim qadamlari

-36x ni olish uchun -56x va 20x ni birlashtirish.

$$32x^{2}-36x-35+15x^{2}-40$$

47x^{2} ni olish uchun 32x^{2} va 15x^{2} ni birlashtirish.

$$47x^{2}-36x-35-40$$

-75 olish uchun -35 dan 40 ni ayirish.

$$47x^{2}-36x-75$$

Omil

$$47\left(x-\frac{18-\sqrt{3849}}{47}\right)\left(x-\frac{\sqrt{3849}+18}{47}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-36x ni olish uchun -56x va 20x ni birlashtirish.

$$factor(32x^{2}-36x-35+15x^{2}-40)$$

47x^{2} ni olish uchun 32x^{2} va 15x^{2} ni birlashtirish.

$$factor(47x^{2}-36x-35-40)$$

-75 olish uchun -35 dan 40 ni ayirish.

$$factor(47x^{2}-36x-75)$$

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.

$$47x^{2}-36x-75=0$$

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.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 47\left(-75\right)}}{2\times 47}$$

-36 kvadratini chiqarish.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 47\left(-75\right)}}{2\times 47}$$

-4 ni 47 marotabaga ko'paytirish.

$$x=\frac{-\left(-36\right)±\sqrt{1296-188\left(-75\right)}}{2\times 47}$$

-188 ni -75 marotabaga ko'paytirish.

$$x=\frac{-\left(-36\right)±\sqrt{1296+14100}}{2\times 47}$$

1296 ni 14100 ga qo'shish.

$$x=\frac{-\left(-36\right)±\sqrt{15396}}{2\times 47}$$

15396 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-36\right)±2\sqrt{3849}}{2\times 47}$$

-36 ning teskarisi 36 ga teng.

$$x=\frac{36±2\sqrt{3849}}{2\times 47}$$

2 ni 47 marotabaga ko'paytirish.

$$x=\frac{36±2\sqrt{3849}}{94}$$

x=\frac{36±2\sqrt{3849}}{94} tenglamasini yeching, bunda ± musbat. 36 ni 2\sqrt{3849} ga qo'shish.

$$x=\frac{2\sqrt{3849}+36}{94}$$

36+2\sqrt{3849} ni 94 ga bo'lish.

$$x=\frac{\sqrt{3849}+18}{47}$$

x=\frac{36±2\sqrt{3849}}{94} tenglamasini yeching, bunda ± manfiy. 36 dan 2\sqrt{3849} ni ayirish.

$$x=\frac{36-2\sqrt{3849}}{94}$$

36-2\sqrt{3849} ni 94 ga bo'lish.

$$x=\frac{18-\sqrt{3849}}{47}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{18+\sqrt{3849}}{47} ga va x_{2} uchun \frac{18-\sqrt{3849}}{47} ga bo‘ling.

$$47x^{2}-36x-75=47\left(x-\frac{\sqrt{3849}+18}{47}\right)\left(x-\frac{18-\sqrt{3849}}{47}\right)$$