x^2+1x-14/2 eching

$$x ^ { 2 } + 1 x - \frac { 14 } { 2 }$$

Baholash

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

Yechim qadamlari

7 ni olish uchun 14 ni 2 ga bo‘ling.

$$x^{2}+1x-7$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

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

Omil

$$\left(x-\frac{-\sqrt{29}-1}{2}\right)\left(x-\frac{\sqrt{29}-1}{2}\right)$$

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.

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

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-7\right)}}{2}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-7\right)}}{2}$$

-4 ni -7 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+28}}{2}$$

1 ni 28 ga qo'shish.

$$x=\frac{-1±\sqrt{29}}{2}$$

x=\frac{-1±\sqrt{29}}{2} tenglamasini yeching, bunda ± musbat. -1 ni \sqrt{29} ga qo'shish.

$$x=\frac{\sqrt{29}-1}{2}$$

x=\frac{-1±\sqrt{29}}{2} tenglamasini yeching, bunda ± manfiy. -1 dan \sqrt{29} ni ayirish.

$$x=\frac{-\sqrt{29}-1}{2}$$

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{29}}{2} ga va x_{2} uchun \frac{-1-\sqrt{29}}{2} ga bo‘ling.

$$x^{2}+x-7=\left(x-\frac{\sqrt{29}-1}{2}\right)\left(x-\frac{-\sqrt{29}-1}{2}\right)$$