-x^2+50x-40 eching

$$- x ^ { 2 } + 50 x - 40$$

Omil

$$-\left(x-\left(25-3\sqrt{65}\right)\right)\left(x-\left(3\sqrt{65}+25\right)\right)$$

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.

$$-x^{2}+50x-40=0$$

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.

$$x=\frac{-50±\sqrt{50^{2}-4\left(-1\right)\left(-40\right)}}{2\left(-1\right)}$$

50 kvadratini chiqarish.

$$x=\frac{-50±\sqrt{2500-4\left(-1\right)\left(-40\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-50±\sqrt{2500+4\left(-40\right)}}{2\left(-1\right)}$$

4 ni -40 marotabaga ko'paytirish.

$$x=\frac{-50±\sqrt{2500-160}}{2\left(-1\right)}$$

2500 ni -160 ga qo'shish.

$$x=\frac{-50±\sqrt{2340}}{2\left(-1\right)}$$

2340 ning kvadrat ildizini chiqarish.

$$x=\frac{-50±6\sqrt{65}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-50±6\sqrt{65}}{-2}$$

x=\frac{-50±6\sqrt{65}}{-2} tenglamasini yeching, bunda ± musbat. -50 ni 6\sqrt{65} ga qo'shish.

$$x=\frac{6\sqrt{65}-50}{-2}$$

-50+6\sqrt{65} ni -2 ga bo'lish.

$$x=25-3\sqrt{65}$$

x=\frac{-50±6\sqrt{65}}{-2} tenglamasini yeching, bunda ± manfiy. -50 dan 6\sqrt{65} ni ayirish.

$$x=\frac{-6\sqrt{65}-50}{-2}$$

-50-6\sqrt{65} ni -2 ga bo'lish.

$$x=3\sqrt{65}+25$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 25-3\sqrt{65} ga va x_{2} uchun 25+3\sqrt{65} ga bo‘ling.

$$-x^{2}+50x-40=-\left(x-\left(25-3\sqrt{65}\right)\right)\left(x-\left(3\sqrt{65}+25\right)\right)$$

Baholash

$$-x^{2}+50x-40$$