x(-11x/5)+5(-11x/5)=22 eching

$$x(- \frac{ 11x }{ 5 } )+5(- \frac{ 11x }{ 5 } )=22$$

x uchun yechish (complex solution)

$$x=\frac{-5+\sqrt{15}i}{2}\approx -2,5+1,936491673i$$

$$x=\frac{-\sqrt{15}i-5}{2}\approx -2,5-1,936491673i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 5 ga ko'paytirish.

$$5x\left(-\frac{11x}{5}\right)+25\left(-\frac{11x}{5}\right)=110$$

5\left(-\frac{11x}{5}\right) ni yagona kasrga aylantiring.

$$\frac{-5\times 11x}{5}x+25\left(-\frac{11x}{5}\right)=110$$

5 va 5 ni qisqartiring.

$$-11xx+25\left(-\frac{11x}{5}\right)=110$$

25 va 5 ichida eng katta umumiy 5 faktorini bekor qiling.

$$-11xx-5\times 11x=110$$

-11 hosil qilish uchun -1 va 11 ni ko'paytirish. -55 hosil qilish uchun -5 va 11 ni ko'paytirish.

$$-11xx-55x=110$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$-11x^{2}-55x=110$$

Ikkala tarafdan 110 ni ayirish.

$$-11x^{2}-55x-110=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -11 ni a, -55 ni b va -110 ni c bilan almashtiring.

$$x=\frac{-\left(-55\right)±\sqrt{\left(-55\right)^{2}-4\left(-11\right)\left(-110\right)}}{2\left(-11\right)}$$

-55 kvadratini chiqarish.

$$x=\frac{-\left(-55\right)±\sqrt{3025-4\left(-11\right)\left(-110\right)}}{2\left(-11\right)}$$

-4 ni -11 marotabaga ko'paytirish.

$$x=\frac{-\left(-55\right)±\sqrt{3025+44\left(-110\right)}}{2\left(-11\right)}$$

44 ni -110 marotabaga ko'paytirish.

$$x=\frac{-\left(-55\right)±\sqrt{3025-4840}}{2\left(-11\right)}$$

3025 ni -4840 ga qo'shish.

$$x=\frac{-\left(-55\right)±\sqrt{-1815}}{2\left(-11\right)}$$

-1815 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-55\right)±11\sqrt{15}i}{2\left(-11\right)}$$

-55 ning teskarisi 55 ga teng.

$$x=\frac{55±11\sqrt{15}i}{2\left(-11\right)}$$

2 ni -11 marotabaga ko'paytirish.

$$x=\frac{55±11\sqrt{15}i}{-22}$$

x=\frac{55±11\sqrt{15}i}{-22} tenglamasini yeching, bunda ± musbat. 55 ni 11i\sqrt{15} ga qo'shish.

$$x=\frac{55+11\sqrt{15}i}{-22}$$

55+11i\sqrt{15} ni -22 ga bo'lish.

$$x=\frac{-\sqrt{15}i-5}{2}$$

x=\frac{55±11\sqrt{15}i}{-22} tenglamasini yeching, bunda ± manfiy. 55 dan 11i\sqrt{15} ni ayirish.

$$x=\frac{-11\sqrt{15}i+55}{-22}$$

55-11i\sqrt{15} ni -22 ga bo'lish.

$$x=\frac{-5+\sqrt{15}i}{2}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{15}i-5}{2} x=\frac{-5+\sqrt{15}i}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 5 ga ko'paytirish.

$$5x\left(-\frac{11x}{5}\right)+25\left(-\frac{11x}{5}\right)=110$$

5\left(-\frac{11x}{5}\right) ni yagona kasrga aylantiring.

$$\frac{-5\times 11x}{5}x+25\left(-\frac{11x}{5}\right)=110$$

5 va 5 ni qisqartiring.

$$-11xx+25\left(-\frac{11x}{5}\right)=110$$

25 va 5 ichida eng katta umumiy 5 faktorini bekor qiling.

$$-11xx-5\times 11x=110$$

-11 hosil qilish uchun -1 va 11 ni ko'paytirish. -55 hosil qilish uchun -5 va 11 ni ko'paytirish.

$$-11xx-55x=110$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$-11x^{2}-55x=110$$

Ikki tarafini -11 ga bo‘ling.

$$\frac{-11x^{2}-55x}{-11}=\frac{110}{-11}$$

-11 ga bo'lish -11 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{55}{-11}\right)x=\frac{110}{-11}$$

-55 ni -11 ga bo'lish.

$$x^{2}+5x=\frac{110}{-11}$$

110 ni -11 ga bo'lish.

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

5 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{2} olish uchun. Keyin, \frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{2} kvadratini chiqarish.

$$x^{2}+5x+\frac{25}{4}=-10+\frac{25}{4}$$

-10 ni \frac{25}{4} ga qo'shish.

$$x^{2}+5x+\frac{25}{4}=-\frac{15}{4}$$

x^{2}+5x+\frac{25}{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.

$$\left(x+\frac{5}{2}\right)^{2}=-\frac{15}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{-\frac{15}{4}}$$

Qisqartirish.

$$x+\frac{5}{2}=\frac{\sqrt{15}i}{2} x+\frac{5}{2}=-\frac{\sqrt{15}i}{2}$$

Tenglamaning ikkala tarafidan \frac{5}{2} ni ayirish.

$$x=\frac{-5+\sqrt{15}i}{2} x=\frac{-\sqrt{15}i-5}{2}$$