3x^2-50x-26 eching

$$3 { x }^{ 2 } -50x-26$$

Omil

$$3\left(x-\frac{25-\sqrt{703}}{3}\right)\left(x-\frac{\sqrt{703}+25}{3}\right)$$

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.

$$3x^{2}-50x-26=0$$

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.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 3\left(-26\right)}}{2\times 3}$$

-50 kvadratini chiqarish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 3\left(-26\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-12\left(-26\right)}}{2\times 3}$$

-12 ni -26 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500+312}}{2\times 3}$$

2500 ni 312 ga qo'shish.

$$x=\frac{-\left(-50\right)±\sqrt{2812}}{2\times 3}$$

2812 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-50\right)±2\sqrt{703}}{2\times 3}$$

-50 ning teskarisi 50 ga teng.

$$x=\frac{50±2\sqrt{703}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{50±2\sqrt{703}}{6}$$

x=\frac{50±2\sqrt{703}}{6} tenglamasini yeching, bunda ± musbat. 50 ni 2\sqrt{703} ga qo'shish.

$$x=\frac{2\sqrt{703}+50}{6}$$

50+2\sqrt{703} ni 6 ga bo'lish.

$$x=\frac{\sqrt{703}+25}{3}$$

x=\frac{50±2\sqrt{703}}{6} tenglamasini yeching, bunda ± manfiy. 50 dan 2\sqrt{703} ni ayirish.

$$x=\frac{50-2\sqrt{703}}{6}$$

50-2\sqrt{703} ni 6 ga bo'lish.

$$x=\frac{25-\sqrt{703}}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{25+\sqrt{703}}{3} ga va x_{2} uchun \frac{25-\sqrt{703}}{3} ga bo‘ling.

$$3x^{2}-50x-26=3\left(x-\frac{\sqrt{703}+25}{3}\right)\left(x-\frac{25-\sqrt{703}}{3}\right)$$

Baholash

$$3x^{2}-50x-26$$