x^2+5x-14quadtext{2}quad3x^2+20x+25 eching

$$x ^ { 2 } + 5 x - 14 \quad \text { 2 } \quad 3 x ^ { 2 } + 20 x + 25$$

Baholash

$$25+25x-83x^{2}$$

Yechim qadamlari

28 hosil qilish uchun 14 va 2 ni ko'paytirish.

$$x^{2}+5x-28\times 3x^{2}+20x+25$$

84 hosil qilish uchun 28 va 3 ni ko'paytirish.

$$x^{2}+5x-84x^{2}+20x+25$$

-83x^{2} ni olish uchun x^{2} va -84x^{2} ni birlashtirish.

$$-83x^{2}+5x+20x+25$$

25x ni olish uchun 5x va 20x ni birlashtirish.

$$-83x^{2}+25x+25$$

Omil

$$-83\left(x-\frac{25-5\sqrt{357}}{166}\right)\left(x-\frac{5\sqrt{357}+25}{166}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

28 hosil qilish uchun 14 va 2 ni ko'paytirish.

$$factor(x^{2}+5x-28\times 3x^{2}+20x+25)$$

84 hosil qilish uchun 28 va 3 ni ko'paytirish.

$$factor(x^{2}+5x-84x^{2}+20x+25)$$

-83x^{2} ni olish uchun x^{2} va -84x^{2} ni birlashtirish.

$$factor(-83x^{2}+5x+20x+25)$$

25x ni olish uchun 5x va 20x ni birlashtirish.

$$factor(-83x^{2}+25x+25)$$

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.

$$-83x^{2}+25x+25=0$$

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.

$$x=\frac{-25±\sqrt{25^{2}-4\left(-83\right)\times 25}}{2\left(-83\right)}$$

25 kvadratini chiqarish.

$$x=\frac{-25±\sqrt{625-4\left(-83\right)\times 25}}{2\left(-83\right)}$$

-4 ni -83 marotabaga ko'paytirish.

$$x=\frac{-25±\sqrt{625+332\times 25}}{2\left(-83\right)}$$

332 ni 25 marotabaga ko'paytirish.

$$x=\frac{-25±\sqrt{625+8300}}{2\left(-83\right)}$$

625 ni 8300 ga qo'shish.

$$x=\frac{-25±\sqrt{8925}}{2\left(-83\right)}$$

8925 ning kvadrat ildizini chiqarish.

$$x=\frac{-25±5\sqrt{357}}{2\left(-83\right)}$$

2 ni -83 marotabaga ko'paytirish.

$$x=\frac{-25±5\sqrt{357}}{-166}$$

x=\frac{-25±5\sqrt{357}}{-166} tenglamasini yeching, bunda ± musbat. -25 ni 5\sqrt{357} ga qo'shish.

$$x=\frac{5\sqrt{357}-25}{-166}$$

-25+5\sqrt{357} ni -166 ga bo'lish.

$$x=\frac{25-5\sqrt{357}}{166}$$

x=\frac{-25±5\sqrt{357}}{-166} tenglamasini yeching, bunda ± manfiy. -25 dan 5\sqrt{357} ni ayirish.

$$x=\frac{-5\sqrt{357}-25}{-166}$$

-25-5\sqrt{357} ni -166 ga bo'lish.

$$x=\frac{5\sqrt{357}+25}{166}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{25-5\sqrt{357}}{166} ga va x_{2} uchun \frac{25+5\sqrt{357}}{166} ga bo‘ling.

$$-83x^{2}+25x+25=-83\left(x-\frac{25-5\sqrt{357}}{166}\right)\left(x-\frac{5\sqrt{357}+25}{166}\right)$$