x^2-3x^2-45x+50 eching

$${ x }^{ 2 } -3 { x }^{ 2 } -45x+50$$

Omil

$$-2\left(x-\frac{-5\sqrt{97}-45}{4}\right)\left(x-\frac{5\sqrt{97}-45}{4}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2x^{2} ni olish uchun x^{2} va -3x^{2} ni birlashtirish.

$$factor(-2x^{2}-45x+50)$$

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.

$$-2x^{2}-45x+50=0$$

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.

$$x=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

-45 kvadratini chiqarish.

$$x=\frac{-\left(-45\right)±\sqrt{2025-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-45\right)±\sqrt{2025+8\times 50}}{2\left(-2\right)}$$

8 ni 50 marotabaga ko'paytirish.

$$x=\frac{-\left(-45\right)±\sqrt{2025+400}}{2\left(-2\right)}$$

2025 ni 400 ga qo'shish.

$$x=\frac{-\left(-45\right)±\sqrt{2425}}{2\left(-2\right)}$$

2425 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-45\right)±5\sqrt{97}}{2\left(-2\right)}$$

-45 ning teskarisi 45 ga teng.

$$x=\frac{45±5\sqrt{97}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{45±5\sqrt{97}}{-4}$$

x=\frac{45±5\sqrt{97}}{-4} tenglamasini yeching, bunda ± musbat. 45 ni 5\sqrt{97} ga qo'shish.

$$x=\frac{5\sqrt{97}+45}{-4}$$

45+5\sqrt{97} ni -4 ga bo'lish.

$$x=\frac{-5\sqrt{97}-45}{4}$$

x=\frac{45±5\sqrt{97}}{-4} tenglamasini yeching, bunda ± manfiy. 45 dan 5\sqrt{97} ni ayirish.

$$x=\frac{45-5\sqrt{97}}{-4}$$

45-5\sqrt{97} ni -4 ga bo'lish.

$$x=\frac{5\sqrt{97}-45}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-45-5\sqrt{97}}{4} ga va x_{2} uchun \frac{-45+5\sqrt{97}}{4} ga bo‘ling.

$$-2x^{2}-45x+50=-2\left(x-\frac{-5\sqrt{97}-45}{4}\right)\left(x-\frac{5\sqrt{97}-45}{4}\right)$$

Baholash

$$50-45x-2x^{2}$$

Yechim qadamlari

-2x^{2} ni olish uchun x^{2} va -3x^{2} ni birlashtirish.

$$-2x^{2}-45x+50$$