-10x^2-x+8x-7+15x^2-9 eching

$$- 10 x ^ { 2 } - x + 8 x - 7 + 15 x ^ { 2 } - 9$$

Baholash

$$5x^{2}+7x-16$$

Yechim qadamlari

7x ni olish uchun -x va 8x ni birlashtirish.

$$-10x^{2}+7x-7+15x^{2}-9$$

5x^{2} ni olish uchun -10x^{2} va 15x^{2} ni birlashtirish.

$$5x^{2}+7x-7-9$$

-16 olish uchun -7 dan 9 ni ayirish.

$$5x^{2}+7x-16$$

Omil

$$5\left(x-\frac{-3\sqrt{41}-7}{10}\right)\left(x-\frac{3\sqrt{41}-7}{10}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

7x ni olish uchun -x va 8x ni birlashtirish.

$$factor(-10x^{2}+7x-7+15x^{2}-9)$$

5x^{2} ni olish uchun -10x^{2} va 15x^{2} ni birlashtirish.

$$factor(5x^{2}+7x-7-9)$$

-16 olish uchun -7 dan 9 ni ayirish.

$$factor(5x^{2}+7x-16)$$

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.

$$5x^{2}+7x-16=0$$

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.

$$x=\frac{-7±\sqrt{7^{2}-4\times 5\left(-16\right)}}{2\times 5}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\times 5\left(-16\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49-20\left(-16\right)}}{2\times 5}$$

-20 ni -16 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+320}}{2\times 5}$$

49 ni 320 ga qo'shish.

$$x=\frac{-7±\sqrt{369}}{2\times 5}$$

369 ning kvadrat ildizini chiqarish.

$$x=\frac{-7±3\sqrt{41}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-7±3\sqrt{41}}{10}$$

x=\frac{-7±3\sqrt{41}}{10} tenglamasini yeching, bunda ± musbat. -7 ni 3\sqrt{41} ga qo'shish.

$$x=\frac{3\sqrt{41}-7}{10}$$

x=\frac{-7±3\sqrt{41}}{10} tenglamasini yeching, bunda ± manfiy. -7 dan 3\sqrt{41} ni ayirish.

$$x=\frac{-3\sqrt{41}-7}{10}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-7+3\sqrt{41}}{10} ga va x_{2} uchun \frac{-7-3\sqrt{41}}{10} ga bo‘ling.

$$5x^{2}+7x-16=5\left(x-\frac{3\sqrt{41}-7}{10}\right)\left(x-\frac{-3\sqrt{41}-7}{10}\right)$$