2x^2-10x+7= eching

$$2 x ^ { 2 } - 10 x + 7 =$$

Omil

$$2\left(x-\frac{5-\sqrt{11}}{2}\right)\left(x-\frac{\sqrt{11}+5}{2}\right)$$

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.

$$2x^{2}-10x+7=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\times 7}}{2\times 2}$$

-10 kvadratini chiqarish.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 2\times 7}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-10\right)±\sqrt{100-8\times 7}}{2\times 2}$$

-8 ni 7 marotabaga ko'paytirish.

$$x=\frac{-\left(-10\right)±\sqrt{100-56}}{2\times 2}$$

100 ni -56 ga qo'shish.

$$x=\frac{-\left(-10\right)±\sqrt{44}}{2\times 2}$$

44 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-10\right)±2\sqrt{11}}{2\times 2}$$

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±2\sqrt{11}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{10±2\sqrt{11}}{4}$$

x=\frac{10±2\sqrt{11}}{4} tenglamasini yeching, bunda ± musbat. 10 ni 2\sqrt{11} ga qo'shish.

$$x=\frac{2\sqrt{11}+10}{4}$$

10+2\sqrt{11} ni 4 ga bo'lish.

$$x=\frac{\sqrt{11}+5}{2}$$

x=\frac{10±2\sqrt{11}}{4} tenglamasini yeching, bunda ± manfiy. 10 dan 2\sqrt{11} ni ayirish.

$$x=\frac{10-2\sqrt{11}}{4}$$

10-2\sqrt{11} ni 4 ga bo'lish.

$$x=\frac{5-\sqrt{11}}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5+\sqrt{11}}{2} ga va x_{2} uchun \frac{5-\sqrt{11}}{2} ga bo‘ling.

$$2x^{2}-10x+7=2\left(x-\frac{\sqrt{11}+5}{2}\right)\left(x-\frac{5-\sqrt{11}}{2}\right)$$

Baholash

$$2x^{2}-10x+7$$