x^2+3x-65= eching

$${ x }^{ 2 } +3x-65=$$

Omil

$$\left(x-\frac{-\sqrt{269}-3}{2}\right)\left(x-\frac{\sqrt{269}-3}{2}\right)$$

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.

$$x^{2}+3x-65=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-65\right)}}{2}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\left(-65\right)}}{2}$$

-4 ni -65 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+260}}{2}$$

9 ni 260 ga qo'shish.

$$x=\frac{-3±\sqrt{269}}{2}$$

x=\frac{-3±\sqrt{269}}{2} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{269} ga qo'shish.

$$x=\frac{\sqrt{269}-3}{2}$$

x=\frac{-3±\sqrt{269}}{2} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{269} ni ayirish.

$$x=\frac{-\sqrt{269}-3}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-3+\sqrt{269}}{2} ga va x_{2} uchun \frac{-3-\sqrt{269}}{2} ga bo‘ling.

$$x^{2}+3x-65=\left(x-\frac{\sqrt{269}-3}{2}\right)\left(x-\frac{-\sqrt{269}-3}{2}\right)$$

Baholash

$$x^{2}+3x-65$$