4x^2-7x-3 eching

$$4 { x }^{ 2 } -7x-3$$

Omil

$$4\left(x-\frac{7-\sqrt{97}}{8}\right)\left(x-\frac{\sqrt{97}+7}{8}\right)$$

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.

$$4x^{2}-7x-3=0$$

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.

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

-7 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49-16\left(-3\right)}}{2\times 4}$$

-16 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+48}}{2\times 4}$$

49 ni 48 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{97}}{2\times 4}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±\sqrt{97}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{7±\sqrt{97}}{8}$$

x=\frac{7±\sqrt{97}}{8} tenglamasini yeching, bunda ± musbat. 7 ni \sqrt{97} ga qo'shish.

$$x=\frac{\sqrt{97}+7}{8}$$

x=\frac{7±\sqrt{97}}{8} tenglamasini yeching, bunda ± manfiy. 7 dan \sqrt{97} ni ayirish.

$$x=\frac{7-\sqrt{97}}{8}$$

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{97}}{8} ga va x_{2} uchun \frac{7-\sqrt{97}}{8} ga bo‘ling.

$$4x^{2}-7x-3=4\left(x-\frac{\sqrt{97}+7}{8}\right)\left(x-\frac{7-\sqrt{97}}{8}\right)$$

Baholash

$$4x^{2}-7x-3$$