(-2t^2-7t+5)+(-8t^2+4t-3) eching

$$( - 2 t ^ { 2 } - 7 t + 5 ) + ( - 8 t ^ { 2 } + 4 t - 3 )$$

Baholash

$$2-3t-10t^{2}$$

Yechim qadamlari

-10t^{2} ni olish uchun -2t^{2} va -8t^{2} ni birlashtirish.

$$-10t^{2}-7t+5+4t-3$$

-3t ni olish uchun -7t va 4t ni birlashtirish.

$$-10t^{2}-3t+5-3$$

2 olish uchun 5 dan 3 ni ayirish.

$$-10t^{2}-3t+2$$

Omil

$$-10\left(t-\frac{-\sqrt{89}-3}{20}\right)\left(t-\frac{\sqrt{89}-3}{20}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-10t^{2} ni olish uchun -2t^{2} va -8t^{2} ni birlashtirish.

$$factor(-10t^{2}-7t+5+4t-3)$$

-3t ni olish uchun -7t va 4t ni birlashtirish.

$$factor(-10t^{2}-3t+5-3)$$

2 olish uchun 5 dan 3 ni ayirish.

$$factor(-10t^{2}-3t+2)$$

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.

$$-10t^{2}-3t+2=0$$

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.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-10\right)\times 2}}{2\left(-10\right)}$$

-3 kvadratini chiqarish.

$$t=\frac{-\left(-3\right)±\sqrt{9-4\left(-10\right)\times 2}}{2\left(-10\right)}$$

-4 ni -10 marotabaga ko'paytirish.

$$t=\frac{-\left(-3\right)±\sqrt{9+40\times 2}}{2\left(-10\right)}$$

40 ni 2 marotabaga ko'paytirish.

$$t=\frac{-\left(-3\right)±\sqrt{9+80}}{2\left(-10\right)}$$

9 ni 80 ga qo'shish.

$$t=\frac{-\left(-3\right)±\sqrt{89}}{2\left(-10\right)}$$

-3 ning teskarisi 3 ga teng.

$$t=\frac{3±\sqrt{89}}{2\left(-10\right)}$$

2 ni -10 marotabaga ko'paytirish.

$$t=\frac{3±\sqrt{89}}{-20}$$

t=\frac{3±\sqrt{89}}{-20} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{89} ga qo'shish.

$$t=\frac{\sqrt{89}+3}{-20}$$

3+\sqrt{89} ni -20 ga bo'lish.

$$t=\frac{-\sqrt{89}-3}{20}$$

t=\frac{3±\sqrt{89}}{-20} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{89} ni ayirish.

$$t=\frac{3-\sqrt{89}}{-20}$$

3-\sqrt{89} ni -20 ga bo'lish.

$$t=\frac{\sqrt{89}-3}{20}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-3-\sqrt{89}}{20} ga va x_{2} uchun \frac{-3+\sqrt{89}}{20} ga bo‘ling.

$$-10t^{2}-3t+2=-10\left(t-\frac{-\sqrt{89}-3}{20}\right)\left(t-\frac{\sqrt{89}-3}{20}\right)$$