x^2+100x-560 eching

$$x ^ { 2 } + 100 x - 560$$

Omil

$$\left(x-\left(-6\sqrt{85}-50\right)\right)\left(x-\left(6\sqrt{85}-50\right)\right)$$

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.

$$x^{2}+100x-560=0$$

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.

$$x=\frac{-100±\sqrt{100^{2}-4\left(-560\right)}}{2}$$

100 kvadratini chiqarish.

$$x=\frac{-100±\sqrt{10000-4\left(-560\right)}}{2}$$

-4 ni -560 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000+2240}}{2}$$

10000 ni 2240 ga qo'shish.

$$x=\frac{-100±\sqrt{12240}}{2}$$

12240 ning kvadrat ildizini chiqarish.

$$x=\frac{-100±12\sqrt{85}}{2}$$

x=\frac{-100±12\sqrt{85}}{2} tenglamasini yeching, bunda ± musbat. -100 ni 12\sqrt{85} ga qo'shish.

$$x=\frac{12\sqrt{85}-100}{2}$$

-100+12\sqrt{85} ni 2 ga bo'lish.

$$x=6\sqrt{85}-50$$

x=\frac{-100±12\sqrt{85}}{2} tenglamasini yeching, bunda ± manfiy. -100 dan 12\sqrt{85} ni ayirish.

$$x=\frac{-12\sqrt{85}-100}{2}$$

-100-12\sqrt{85} ni 2 ga bo'lish.

$$x=-6\sqrt{85}-50$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -50+6\sqrt{85} ga va x_{2} uchun -50-6\sqrt{85} ga bo‘ling.

$$x^{2}+100x-560=\left(x-\left(6\sqrt{85}-50\right)\right)\left(x-\left(-6\sqrt{85}-50\right)\right)$$

Baholash

$$x^{2}+100x-560$$