59x-3x^2-3x+12 eching

$$59x-3 { x }^{ 2 } -3x+12$$

Omil

$$-3\left(x-\frac{28-2\sqrt{205}}{3}\right)\left(x-\frac{2\sqrt{205}+28}{3}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

56x ni olish uchun 59x va -3x ni birlashtirish.

$$factor(56x-3x^{2}+12)$$

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.

$$-3x^{2}+56x+12=0$$

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.

$$x=\frac{-56±\sqrt{56^{2}-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

56 kvadratini chiqarish.

$$x=\frac{-56±\sqrt{3136-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-56±\sqrt{3136+12\times 12}}{2\left(-3\right)}$$

12 ni 12 marotabaga ko'paytirish.

$$x=\frac{-56±\sqrt{3136+144}}{2\left(-3\right)}$$

3136 ni 144 ga qo'shish.

$$x=\frac{-56±\sqrt{3280}}{2\left(-3\right)}$$

3280 ning kvadrat ildizini chiqarish.

$$x=\frac{-56±4\sqrt{205}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-56±4\sqrt{205}}{-6}$$

x=\frac{-56±4\sqrt{205}}{-6} tenglamasini yeching, bunda ± musbat. -56 ni 4\sqrt{205} ga qo'shish.

$$x=\frac{4\sqrt{205}-56}{-6}$$

-56+4\sqrt{205} ni -6 ga bo'lish.

$$x=\frac{28-2\sqrt{205}}{3}$$

x=\frac{-56±4\sqrt{205}}{-6} tenglamasini yeching, bunda ± manfiy. -56 dan 4\sqrt{205} ni ayirish.

$$x=\frac{-4\sqrt{205}-56}{-6}$$

-56-4\sqrt{205} ni -6 ga bo'lish.

$$x=\frac{2\sqrt{205}+28}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{28-2\sqrt{205}}{3} ga va x_{2} uchun \frac{28+2\sqrt{205}}{3} ga bo‘ling.

$$-3x^{2}+56x+12=-3\left(x-\frac{28-2\sqrt{205}}{3}\right)\left(x-\frac{2\sqrt{205}+28}{3}\right)$$

Baholash

$$12+56x-3x^{2}$$

Yechim qadamlari

56x ni olish uchun 59x va -3x ni birlashtirish.

$$56x-3x^{2}+12$$