25x^2+50x-6000= eching

$$25 x ^ { 2 } + 50 x - 6000 =$$

Omil

$$25\left(x-\left(-\sqrt{241}-1\right)\right)\left(x-\left(\sqrt{241}-1\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$25x^{2}+50x-6000=0$$

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.

$$x=\frac{-50±\sqrt{50^{2}-4\times 25\left(-6000\right)}}{2\times 25}$$

50 kvadratini chiqarish.

$$x=\frac{-50±\sqrt{2500-4\times 25\left(-6000\right)}}{2\times 25}$$

-4 ni 25 marotabaga ko'paytirish.

$$x=\frac{-50±\sqrt{2500-100\left(-6000\right)}}{2\times 25}$$

-100 ni -6000 marotabaga ko'paytirish.

$$x=\frac{-50±\sqrt{2500+600000}}{2\times 25}$$

2500 ni 600000 ga qo'shish.

$$x=\frac{-50±\sqrt{602500}}{2\times 25}$$

602500 ning kvadrat ildizini chiqarish.

$$x=\frac{-50±50\sqrt{241}}{2\times 25}$$

2 ni 25 marotabaga ko'paytirish.

$$x=\frac{-50±50\sqrt{241}}{50}$$

x=\frac{-50±50\sqrt{241}}{50} tenglamasini yeching, bunda ± musbat. -50 ni 50\sqrt{241} ga qo'shish.

$$x=\frac{50\sqrt{241}-50}{50}$$

-50+50\sqrt{241} ni 50 ga bo'lish.

$$x=\sqrt{241}-1$$

x=\frac{-50±50\sqrt{241}}{50} tenglamasini yeching, bunda ± manfiy. -50 dan 50\sqrt{241} ni ayirish.

$$x=\frac{-50\sqrt{241}-50}{50}$$

-50-50\sqrt{241} ni 50 ga bo'lish.

$$x=-\sqrt{241}-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -1+\sqrt{241} ga va x_{2} uchun -1-\sqrt{241} ga bo‘ling.

$$25x^{2}+50x-6000=25\left(x-\left(\sqrt{241}-1\right)\right)\left(x-\left(-\sqrt{241}-1\right)\right)$$

Baholash

$$25\left(x^{2}+2x-240\right)$$