-9x^2+6+11x^2-13-7x eching

$$- 9 x ^ { 2 } + 6 + 11 x ^ { 2 } - 13 - 7 x$$

Baholash

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

Yechim qadamlari

2x^{2} ni olish uchun -9x^{2} va 11x^{2} ni birlashtirish.

$$2x^{2}+6-13-7x$$

-7 olish uchun 6 dan 13 ni ayirish.

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

Omil

$$2\left(x-\frac{7-\sqrt{105}}{4}\right)\left(x-\frac{\sqrt{105}+7}{4}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x^{2} ni olish uchun -9x^{2} va 11x^{2} ni birlashtirish.

$$factor(2x^{2}+6-13-7x)$$

-7 olish uchun 6 dan 13 ni ayirish.

$$factor(2x^{2}-7-7x)$$

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.

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

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.

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

-7 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49-8\left(-7\right)}}{2\times 2}$$

-8 ni -7 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+56}}{2\times 2}$$

49 ni 56 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{105}}{2\times 2}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±\sqrt{105}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{7±\sqrt{105}}{4}$$

x=\frac{7±\sqrt{105}}{4} tenglamasini yeching, bunda ± musbat. 7 ni \sqrt{105} ga qo'shish.

$$x=\frac{\sqrt{105}+7}{4}$$

x=\frac{7±\sqrt{105}}{4} tenglamasini yeching, bunda ± manfiy. 7 dan \sqrt{105} ni ayirish.

$$x=\frac{7-\sqrt{105}}{4}$$

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{105}}{4} ga va x_{2} uchun \frac{7-\sqrt{105}}{4} ga bo‘ling.

$$2x^{2}-7x-7=2\left(x-\frac{\sqrt{105}+7}{4}\right)\left(x-\frac{7-\sqrt{105}}{4}\right)$$