2x-(x+1)^2=x^2-9 eching

$$2 x - ( x + 1 ) ^ { 2 } = x ^ { 2 } - 9$$

x uchun yechish

$$x=2$$

$$x=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$2x-\left(x^{2}+2x+1\right)=x^{2}-9$$

x^{2}+2x+1 teskarisini topish uchun har birining teskarisini toping.

$$2x-x^{2}-2x-1=x^{2}-9$$

0 ni olish uchun 2x va -2x ni birlashtirish.

$$-x^{2}-1=x^{2}-9$$

Ikkala tarafdan x^{2} ni ayirish.

$$-x^{2}-1-x^{2}=-9$$

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

$$-2x^{2}-1=-9$$

1 ni ikki tarafga qo’shing.

$$-2x^{2}=-9+1$$

-8 olish uchun -9 va 1'ni qo'shing.

$$-2x^{2}=-8$$

Ikki tarafini -2 ga bo‘ling.

$$x^{2}=\frac{-8}{-2}$$

4 ni olish uchun -8 ni -2 ga bo‘ling.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$2x-\left(x^{2}+2x+1\right)=x^{2}-9$$

x^{2}+2x+1 teskarisini topish uchun har birining teskarisini toping.

$$2x-x^{2}-2x-1=x^{2}-9$$

0 ni olish uchun 2x va -2x ni birlashtirish.

$$-x^{2}-1=x^{2}-9$$

Ikkala tarafdan x^{2} ni ayirish.

$$-x^{2}-1-x^{2}=-9$$

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

$$-2x^{2}-1=-9$$

9 ni ikki tarafga qo’shing.

$$-2x^{2}-1+9=0$$

8 olish uchun -1 va 9'ni qo'shing.

$$-2x^{2}+8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 0 ni b va 8 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 8}}{2\left(-2\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 8}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{8\times 8}}{2\left(-2\right)}$$

8 ni 8 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{64}}{2\left(-2\right)}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±8}{-4}$$

x=\frac{0±8}{-4} tenglamasini yeching, bunda ± musbat. 8 ni -4 ga bo'lish.

$$x=-2$$

x=\frac{0±8}{-4} tenglamasini yeching, bunda ± manfiy. -8 ni -4 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=-2 x=2$$