33x^2+74x+7-39x^2-88x+80 eching

$$33 x ^ { 2 } + 74 x + 7 - 39 x ^ { 2 } - 88 x + 80$$

Baholash

$$87-14x-6x^{2}$$

Yechim qadamlari

-6x^{2} ni olish uchun 33x^{2} va -39x^{2} ni birlashtirish.

$$-6x^{2}+74x+7-88x+80$$

-14x ni olish uchun 74x va -88x ni birlashtirish.

$$-6x^{2}-14x+7+80$$

87 olish uchun 7 va 80'ni qo'shing.

$$-6x^{2}-14x+87$$

Omil

$$-6\left(x-\frac{-\sqrt{571}-7}{6}\right)\left(x-\frac{\sqrt{571}-7}{6}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-6x^{2} ni olish uchun 33x^{2} va -39x^{2} ni birlashtirish.

$$factor(-6x^{2}+74x+7-88x+80)$$

-14x ni olish uchun 74x va -88x ni birlashtirish.

$$factor(-6x^{2}-14x+7+80)$$

87 olish uchun 7 va 80'ni qo'shing.

$$factor(-6x^{2}-14x+87)$$

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.

$$-6x^{2}-14x+87=0$$

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.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\left(-6\right)\times 87}}{2\left(-6\right)}$$

-14 kvadratini chiqarish.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\left(-6\right)\times 87}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-14\right)±\sqrt{196+24\times 87}}{2\left(-6\right)}$$

24 ni 87 marotabaga ko'paytirish.

$$x=\frac{-\left(-14\right)±\sqrt{196+2088}}{2\left(-6\right)}$$

196 ni 2088 ga qo'shish.

$$x=\frac{-\left(-14\right)±\sqrt{2284}}{2\left(-6\right)}$$

2284 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-14\right)±2\sqrt{571}}{2\left(-6\right)}$$

-14 ning teskarisi 14 ga teng.

$$x=\frac{14±2\sqrt{571}}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$x=\frac{14±2\sqrt{571}}{-12}$$

x=\frac{14±2\sqrt{571}}{-12} tenglamasini yeching, bunda ± musbat. 14 ni 2\sqrt{571} ga qo'shish.

$$x=\frac{2\sqrt{571}+14}{-12}$$

14+2\sqrt{571} ni -12 ga bo'lish.

$$x=\frac{-\sqrt{571}-7}{6}$$

x=\frac{14±2\sqrt{571}}{-12} tenglamasini yeching, bunda ± manfiy. 14 dan 2\sqrt{571} ni ayirish.

$$x=\frac{14-2\sqrt{571}}{-12}$$

14-2\sqrt{571} ni -12 ga bo'lish.

$$x=\frac{\sqrt{571}-7}{6}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-7-\sqrt{571}}{6} ga va x_{2} uchun \frac{-7+\sqrt{571}}{6} ga bo‘ling.

$$-6x^{2}-14x+87=-6\left(x-\frac{-\sqrt{571}-7}{6}\right)\left(x-\frac{\sqrt{571}-7}{6}\right)$$