4x^2+20x+25-x^2-8x+3x-24 eching

$$4 { x }^{ 2 } +20x+25- { x }^{ 2 } -8x+3x-24$$

Baholash

$$3x^{2}+15x+1$$

Yechim qadamlari

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$3x^{2}+20x+25-8x+3x-24$$

12x ni olish uchun 20x va -8x ni birlashtirish.

$$3x^{2}+12x+25+3x-24$$

15x ni olish uchun 12x va 3x ni birlashtirish.

$$3x^{2}+15x+25-24$$

1 olish uchun 25 dan 24 ni ayirish.

$$3x^{2}+15x+1$$

Omil

$$3\left(x-\left(-\frac{\sqrt{213}}{6}-\frac{5}{2}\right)\right)\left(x-\left(\frac{\sqrt{213}}{6}-\frac{5}{2}\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$factor(3x^{2}+20x+25-8x+3x-24)$$

12x ni olish uchun 20x va -8x ni birlashtirish.

$$factor(3x^{2}+12x+25+3x-24)$$

15x ni olish uchun 12x va 3x ni birlashtirish.

$$factor(3x^{2}+15x+25-24)$$

1 olish uchun 25 dan 24 ni ayirish.

$$factor(3x^{2}+15x+1)$$

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.

$$3x^{2}+15x+1=0$$

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.

$$x=\frac{-15±\sqrt{15^{2}-4\times 3}}{2\times 3}$$

15 kvadratini chiqarish.

$$x=\frac{-15±\sqrt{225-4\times 3}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-15±\sqrt{225-12}}{2\times 3}$$

225 ni -12 ga qo'shish.

$$x=\frac{-15±\sqrt{213}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-15±\sqrt{213}}{6}$$

x=\frac{-15±\sqrt{213}}{6} tenglamasini yeching, bunda ± musbat. -15 ni \sqrt{213} ga qo'shish.

$$x=\frac{\sqrt{213}-15}{6}$$

-15+\sqrt{213} ni 6 ga bo'lish.

$$x=\frac{\sqrt{213}}{6}-\frac{5}{2}$$

x=\frac{-15±\sqrt{213}}{6} tenglamasini yeching, bunda ± manfiy. -15 dan \sqrt{213} ni ayirish.

$$x=\frac{-\sqrt{213}-15}{6}$$

-15-\sqrt{213} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{213}}{6}-\frac{5}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{5}{2}+\frac{\sqrt{213}}{6} ga va x_{2} uchun -\frac{5}{2}-\frac{\sqrt{213}}{6} ga bo‘ling.

$$3x^{2}+15x+1=3\left(x-\left(\frac{\sqrt{213}}{6}-\frac{5}{2}\right)\right)\left(x-\left(-\frac{\sqrt{213}}{6}-\frac{5}{2}\right)\right)$$