x^2-10x-25 eching

$$x ^ { 2 } - 10 x - 25$$

Omil

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

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.

$$x^{2}-10x-25=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-25\right)}}{2}$$

-10 kvadratini chiqarish.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\left(-25\right)}}{2}$$

-4 ni -25 marotabaga ko'paytirish.

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

100 ni 100 ga qo'shish.

$$x=\frac{-\left(-10\right)±\sqrt{200}}{2}$$

200 ning kvadrat ildizini chiqarish.

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

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±10\sqrt{2}}{2}$$

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

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

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

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

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

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

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

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

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

$$x^{2}-10x-25=\left(x-\left(5\sqrt{2}+5\right)\right)\left(x-\left(5-5\sqrt{2}\right)\right)$$

Baholash

$$x^{2}-10x-25$$