-5x^2+6x+7+-x^2+4x eching

$$-5 { x }^{ 2 } +6x+7+- { x }^{ 2 } +4x$$

Baholash

$$7+10x-6x^{2}$$

Yechim qadamlari

10x ni olish uchun 6x va 4x ni birlashtirish.

$$-5x^{2}+10x+7-x^{2}$$

-6x^{2} ni olish uchun -5x^{2} va -x^{2} ni birlashtirish.

$$-6x^{2}+10x+7$$

Omil

$$-6\left(x-\frac{5-\sqrt{67}}{6}\right)\left(x-\frac{\sqrt{67}+5}{6}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

10x ni olish uchun 6x va 4x ni birlashtirish.

$$factor(-5x^{2}+10x+7-x^{2})$$

-6x^{2} ni olish uchun -5x^{2} va -x^{2} ni birlashtirish.

$$factor(-6x^{2}+10x+7)$$

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.

$$-6x^{2}+10x+7=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-6\right)\times 7}}{2\left(-6\right)}$$

10 kvadratini chiqarish.

$$x=\frac{-10±\sqrt{100-4\left(-6\right)\times 7}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100+24\times 7}}{2\left(-6\right)}$$

24 ni 7 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100+168}}{2\left(-6\right)}$$

100 ni 168 ga qo'shish.

$$x=\frac{-10±\sqrt{268}}{2\left(-6\right)}$$

268 ning kvadrat ildizini chiqarish.

$$x=\frac{-10±2\sqrt{67}}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$x=\frac{-10±2\sqrt{67}}{-12}$$

x=\frac{-10±2\sqrt{67}}{-12} tenglamasini yeching, bunda ± musbat. -10 ni 2\sqrt{67} ga qo'shish.

$$x=\frac{2\sqrt{67}-10}{-12}$$

-10+2\sqrt{67} ni -12 ga bo'lish.

$$x=\frac{5-\sqrt{67}}{6}$$

x=\frac{-10±2\sqrt{67}}{-12} tenglamasini yeching, bunda ± manfiy. -10 dan 2\sqrt{67} ni ayirish.

$$x=\frac{-2\sqrt{67}-10}{-12}$$

-10-2\sqrt{67} ni -12 ga bo'lish.

$$x=\frac{\sqrt{67}+5}{6}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5-\sqrt{67}}{6} ga va x_{2} uchun \frac{5+\sqrt{67}}{6} ga bo‘ling.

$$-6x^{2}+10x+7=-6\left(x-\frac{5-\sqrt{67}}{6}\right)\left(x-\frac{\sqrt{67}+5}{6}\right)$$