x^2-12x-112 eching

$${ x }^{ 2 } -12x-112$$

Omil

$$\left(x-\left(6-2\sqrt{37}\right)\right)\left(x-\left(2\sqrt{37}+6\right)\right)$$

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.

$$x^{2}-12x-112=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-112\right)}}{2}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-112\right)}}{2}$$

-4 ni -112 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+448}}{2}$$

144 ni 448 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{592}}{2}$$

592 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±4\sqrt{37}}{2}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±4\sqrt{37}}{2}$$

x=\frac{12±4\sqrt{37}}{2} tenglamasini yeching, bunda ± musbat. 12 ni 4\sqrt{37} ga qo'shish.

$$x=\frac{4\sqrt{37}+12}{2}$$

12+4\sqrt{37} ni 2 ga bo'lish.

$$x=2\sqrt{37}+6$$

x=\frac{12±4\sqrt{37}}{2} tenglamasini yeching, bunda ± manfiy. 12 dan 4\sqrt{37} ni ayirish.

$$x=\frac{12-4\sqrt{37}}{2}$$

12-4\sqrt{37} ni 2 ga bo'lish.

$$x=6-2\sqrt{37}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 6+2\sqrt{37} ga va x_{2} uchun 6-2\sqrt{37} ga bo‘ling.

$$x^{2}-12x-112=\left(x-\left(2\sqrt{37}+6\right)\right)\left(x-\left(6-2\sqrt{37}\right)\right)$$

Baholash

$$x^{2}-12x-112$$