4x-10+16-49x^2 eching

$$4 x - 10 + 16 - 49 x ^ { 2 }$$

Omil

$$-49\left(x-\frac{2-\sqrt{298}}{49}\right)\left(x-\frac{\sqrt{298}+2}{49}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

6 olish uchun -10 va 16'ni qo'shing.

$$factor(4x+6-49x^{2})$$

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.

$$-49x^{2}+4x+6=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-49\right)\times 6}}{2\left(-49\right)}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-49\right)\times 6}}{2\left(-49\right)}$$

-4 ni -49 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+196\times 6}}{2\left(-49\right)}$$

196 ni 6 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+1176}}{2\left(-49\right)}$$

16 ni 1176 ga qo'shish.

$$x=\frac{-4±\sqrt{1192}}{2\left(-49\right)}$$

1192 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{298}}{2\left(-49\right)}$$

2 ni -49 marotabaga ko'paytirish.

$$x=\frac{-4±2\sqrt{298}}{-98}$$

x=\frac{-4±2\sqrt{298}}{-98} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{298} ga qo'shish.

$$x=\frac{2\sqrt{298}-4}{-98}$$

-4+2\sqrt{298} ni -98 ga bo'lish.

$$x=\frac{2-\sqrt{298}}{49}$$

x=\frac{-4±2\sqrt{298}}{-98} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{298} ni ayirish.

$$x=\frac{-2\sqrt{298}-4}{-98}$$

-4-2\sqrt{298} ni -98 ga bo'lish.

$$x=\frac{\sqrt{298}+2}{49}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{2-\sqrt{298}}{49} ga va x_{2} uchun \frac{2+\sqrt{298}}{49} ga bo‘ling.

$$-49x^{2}+4x+6=-49\left(x-\frac{2-\sqrt{298}}{49}\right)\left(x-\frac{\sqrt{298}+2}{49}\right)$$

Baholash

$$6+4x-49x^{2}$$

Yechim qadamlari

6 olish uchun -10 va 16'ni qo'shing.

$$4x+6-49x^{2}$$