(2s^2+6s)+(-4s-3) eching

$$( 2 s ^ { 2 } + 6 s ) + ( - 4 s - 3 )$$

Omil

$$2\left(s-\frac{-\sqrt{7}-1}{2}\right)\left(s-\frac{\sqrt{7}-1}{2}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

2s ni olish uchun 6s va -4s ni birlashtirish.

$$factor(2s^{2}+2s-3)$$

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.

$$2s^{2}+2s-3=0$$

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.

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

2 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$s=\frac{-2±\sqrt{4-8\left(-3\right)}}{2\times 2}$$

-8 ni -3 marotabaga ko'paytirish.

$$s=\frac{-2±\sqrt{4+24}}{2\times 2}$$

4 ni 24 ga qo'shish.

$$s=\frac{-2±\sqrt{28}}{2\times 2}$$

28 ning kvadrat ildizini chiqarish.

$$s=\frac{-2±2\sqrt{7}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$s=\frac{-2±2\sqrt{7}}{4}$$

s=\frac{-2±2\sqrt{7}}{4} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{7} ga qo'shish.

$$s=\frac{2\sqrt{7}-2}{4}$$

-2+2\sqrt{7} ni 4 ga bo'lish.

$$s=\frac{\sqrt{7}-1}{2}$$

s=\frac{-2±2\sqrt{7}}{4} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{7} ni ayirish.

$$s=\frac{-2\sqrt{7}-2}{4}$$

-2-2\sqrt{7} ni 4 ga bo'lish.

$$s=\frac{-\sqrt{7}-1}{2}$$

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

$$2s^{2}+2s-3=2\left(s-\frac{\sqrt{7}-1}{2}\right)\left(s-\frac{-\sqrt{7}-1}{2}\right)$$

Baholash

$$2s^{2}+2s-3$$

Yechim qadamlari

2s ni olish uchun 6s va -4s ni birlashtirish.

$$2s^{2}+2s-3$$