(8x^2-2x+1)+(3x^2+5x-8)= eching

$$( 8 x ^ { 2 } - 2 x + 1 ) + ( 3 x ^ { 2 } + 5 x - 8 ) =$$

Baholash

$$11x^{2}+3x-7$$

Yechim qadamlari

11x^{2} ni olish uchun 8x^{2} va 3x^{2} ni birlashtirish.

$$11x^{2}-2x+1+5x-8$$

3x ni olish uchun -2x va 5x ni birlashtirish.

$$11x^{2}+3x+1-8$$

-7 olish uchun 1 dan 8 ni ayirish.

$$11x^{2}+3x-7$$

Omil

$$11\left(x-\frac{-\sqrt{317}-3}{22}\right)\left(x-\frac{\sqrt{317}-3}{22}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

11x^{2} ni olish uchun 8x^{2} va 3x^{2} ni birlashtirish.

$$factor(11x^{2}-2x+1+5x-8)$$

3x ni olish uchun -2x va 5x ni birlashtirish.

$$factor(11x^{2}+3x+1-8)$$

-7 olish uchun 1 dan 8 ni ayirish.

$$factor(11x^{2}+3x-7)$$

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.

$$11x^{2}+3x-7=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 11\left(-7\right)}}{2\times 11}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times 11\left(-7\right)}}{2\times 11}$$

-4 ni 11 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-44\left(-7\right)}}{2\times 11}$$

-44 ni -7 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+308}}{2\times 11}$$

9 ni 308 ga qo'shish.

$$x=\frac{-3±\sqrt{317}}{2\times 11}$$

2 ni 11 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{317}}{22}$$

x=\frac{-3±\sqrt{317}}{22} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{317} ga qo'shish.

$$x=\frac{\sqrt{317}-3}{22}$$

x=\frac{-3±\sqrt{317}}{22} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{317} ni ayirish.

$$x=\frac{-\sqrt{317}-3}{22}$$

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{317}}{22} ga va x_{2} uchun \frac{-3-\sqrt{317}}{22} ga bo‘ling.

$$11x^{2}+3x-7=11\left(x-\frac{\sqrt{317}-3}{22}\right)\left(x-\frac{-\sqrt{317}-3}{22}\right)$$