-(x+1)(x+4)-x+3*x=8 eching

$$- ( x + 1 ) ( x + 4 ) - x + 3 \cdot x = 8$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{39}i-3}{2}\approx -1,5-3,122498999i$$

$$x=\frac{-3+\sqrt{39}i}{2}\approx -1,5+3,122498999i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+1 teskarisini topish uchun har birining teskarisini toping.

$$\left(-x-1\right)\left(x+4\right)-x+3x=8$$

-x-1 ifodaning har bir elementini x+4 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$-x^{2}-4x-x-4-x+3x=8$$

-5x ni olish uchun -4x va -x ni birlashtirish.

$$-x^{2}-5x-4-x+3x=8$$

-6x ni olish uchun -5x va -x ni birlashtirish.

$$-x^{2}-6x-4+3x=8$$

-3x ni olish uchun -6x va 3x ni birlashtirish.

$$-x^{2}-3x-4=8$$

Ikkala tarafdan 8 ni ayirish.

$$-x^{2}-3x-4-8=0$$

-12 olish uchun -4 dan 8 ni ayirish.

$$-x^{2}-3x-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -3 ni b va -12 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-1\right)\left(-12\right)}}{2\left(-1\right)}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-1\right)\left(-12\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+4\left(-12\right)}}{2\left(-1\right)}$$

4 ni -12 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9-48}}{2\left(-1\right)}$$

9 ni -48 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{-39}}{2\left(-1\right)}$$

-39 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{39}i}{2\left(-1\right)}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{39}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{3±\sqrt{39}i}{-2}$$

x=\frac{3±\sqrt{39}i}{-2} tenglamasini yeching, bunda ± musbat. 3 ni i\sqrt{39} ga qo'shish.

$$x=\frac{3+\sqrt{39}i}{-2}$$

3+i\sqrt{39} ni -2 ga bo'lish.

$$x=\frac{-\sqrt{39}i-3}{2}$$

x=\frac{3±\sqrt{39}i}{-2} tenglamasini yeching, bunda ± manfiy. 3 dan i\sqrt{39} ni ayirish.

$$x=\frac{-\sqrt{39}i+3}{-2}$$

3-i\sqrt{39} ni -2 ga bo'lish.

$$x=\frac{-3+\sqrt{39}i}{2}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{39}i-3}{2} x=\frac{-3+\sqrt{39}i}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x+1 teskarisini topish uchun har birining teskarisini toping.

$$\left(-x-1\right)\left(x+4\right)-x+3x=8$$

-x-1 ifodaning har bir elementini x+4 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$-x^{2}-4x-x-4-x+3x=8$$

-5x ni olish uchun -4x va -x ni birlashtirish.

$$-x^{2}-5x-4-x+3x=8$$

-6x ni olish uchun -5x va -x ni birlashtirish.

$$-x^{2}-6x-4+3x=8$$

-3x ni olish uchun -6x va 3x ni birlashtirish.

$$-x^{2}-3x-4=8$$

4 ni ikki tarafga qo’shing.

$$-x^{2}-3x=8+4$$

12 olish uchun 8 va 4'ni qo'shing.

$$-x^{2}-3x=12$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-3x}{-1}=\frac{12}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{3}{-1}\right)x=\frac{12}{-1}$$

-3 ni -1 ga bo'lish.

$$x^{2}+3x=\frac{12}{-1}$$

12 ni -1 ga bo'lish.

$$x^{2}+3x=-12$$

3 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{2} olish uchun. Keyin, \frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=-12+\left(\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.

$$x^{2}+3x+\frac{9}{4}=-12+\frac{9}{4}$$

-12 ni \frac{9}{4} ga qo'shish.

$$x^{2}+3x+\frac{9}{4}=-\frac{39}{4}$$

x^{2}+3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{2}\right)^{2}=-\frac{39}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{-\frac{39}{4}}$$

Qisqartirish.

$$x+\frac{3}{2}=\frac{\sqrt{39}i}{2} x+\frac{3}{2}=-\frac{\sqrt{39}i}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$x=\frac{-3+\sqrt{39}i}{2} x=\frac{-\sqrt{39}i-3}{2}$$