2x^2-64x+25 eching

$$2 x ^ { 2 } - 64 x + 25$$

Omil

$$2\left(x-\left(-\frac{\sqrt{974}}{2}+16\right)\right)\left(x-\left(\frac{\sqrt{974}}{2}+16\right)\right)$$

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.

$$2x^{2}-64x+25=0$$

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.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 2\times 25}}{2\times 2}$$

-64 kvadratini chiqarish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4\times 2\times 25}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-8\times 25}}{2\times 2}$$

-8 ni 25 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-200}}{2\times 2}$$

4096 ni -200 ga qo'shish.

$$x=\frac{-\left(-64\right)±\sqrt{3896}}{2\times 2}$$

3896 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-64\right)±2\sqrt{974}}{2\times 2}$$

-64 ning teskarisi 64 ga teng.

$$x=\frac{64±2\sqrt{974}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{64±2\sqrt{974}}{4}$$

x=\frac{64±2\sqrt{974}}{4} tenglamasini yeching, bunda ± musbat. 64 ni 2\sqrt{974} ga qo'shish.

$$x=\frac{2\sqrt{974}+64}{4}$$

64+2\sqrt{974} ni 4 ga bo'lish.

$$x=\frac{\sqrt{974}}{2}+16$$

x=\frac{64±2\sqrt{974}}{4} tenglamasini yeching, bunda ± manfiy. 64 dan 2\sqrt{974} ni ayirish.

$$x=\frac{64-2\sqrt{974}}{4}$$

64-2\sqrt{974} ni 4 ga bo'lish.

$$x=-\frac{\sqrt{974}}{2}+16$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 16+\frac{\sqrt{974}}{2} ga va x_{2} uchun 16-\frac{\sqrt{974}}{2} ga bo‘ling.

$$2x^{2}-64x+25=2\left(x-\left(\frac{\sqrt{974}}{2}+16\right)\right)\left(x-\left(-\frac{\sqrt{974}}{2}+16\right)\right)$$

Baholash

$$2x^{2}-64x+25$$