x^2-7x-3 eching

$$x ^ { 2 } - 7 x - 3$$

Omil

$$\left(x-\frac{7-\sqrt{61}}{2}\right)\left(x-\frac{\sqrt{61}+7}{2}\right)$$

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.

$$x^{2}-7x-3=0$$

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.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\left(-3\right)}}{2}$$

-7 kvadratini chiqarish.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\left(-3\right)}}{2}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+12}}{2}$$

49 ni 12 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{61}}{2}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±\sqrt{61}}{2}$$

x=\frac{7±\sqrt{61}}{2} tenglamasini yeching, bunda ± musbat. 7 ni \sqrt{61} ga qo'shish.

$$x=\frac{\sqrt{61}+7}{2}$$

x=\frac{7±\sqrt{61}}{2} tenglamasini yeching, bunda ± manfiy. 7 dan \sqrt{61} ni ayirish.

$$x=\frac{7-\sqrt{61}}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{7+\sqrt{61}}{2} ga va x_{2} uchun \frac{7-\sqrt{61}}{2} ga bo‘ling.

$$x^{2}-7x-3=\left(x-\frac{\sqrt{61}+7}{2}\right)\left(x-\frac{7-\sqrt{61}}{2}\right)$$

Baholash

$$x^{2}-7x-3$$