(7-2x)(x-2)=112 eching

$$(7-2x)(x-2)=112$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{887}i+11}{4}\approx 2,75-7,445636306i$$

$$x=\frac{11+\sqrt{887}i}{4}\approx 2,75+7,445636306i$$

Kvadrat tenglamalaridan foydalanish qoidalari

7-2x ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$11x-14-2x^{2}=112$$

Ikkala tarafdan 112 ni ayirish.

$$11x-14-2x^{2}-112=0$$

-126 olish uchun -14 dan 112 ni ayirish.

$$11x-126-2x^{2}=0$$

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.

$$-2x^{2}+11x-126=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 11 ni b va -126 ni c bilan almashtiring.

$$x=\frac{-11±\sqrt{11^{2}-4\left(-2\right)\left(-126\right)}}{2\left(-2\right)}$$

11 kvadratini chiqarish.

$$x=\frac{-11±\sqrt{121-4\left(-2\right)\left(-126\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121+8\left(-126\right)}}{2\left(-2\right)}$$

8 ni -126 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121-1008}}{2\left(-2\right)}$$

121 ni -1008 ga qo'shish.

$$x=\frac{-11±\sqrt{-887}}{2\left(-2\right)}$$

-887 ning kvadrat ildizini chiqarish.

$$x=\frac{-11±\sqrt{887}i}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{887}i}{-4}$$

x=\frac{-11±\sqrt{887}i}{-4} tenglamasini yeching, bunda ± musbat. -11 ni i\sqrt{887} ga qo'shish.

$$x=\frac{-11+\sqrt{887}i}{-4}$$

-11+i\sqrt{887} ni -4 ga bo'lish.

$$x=\frac{-\sqrt{887}i+11}{4}$$

x=\frac{-11±\sqrt{887}i}{-4} tenglamasini yeching, bunda ± manfiy. -11 dan i\sqrt{887} ni ayirish.

$$x=\frac{-\sqrt{887}i-11}{-4}$$

-11-i\sqrt{887} ni -4 ga bo'lish.

$$x=\frac{11+\sqrt{887}i}{4}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{887}i+11}{4} x=\frac{11+\sqrt{887}i}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

7-2x ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$11x-14-2x^{2}=112$$

14 ni ikki tarafga qo’shing.

$$11x-2x^{2}=112+14$$

126 olish uchun 112 va 14'ni qo'shing.

$$11x-2x^{2}=126$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-2x^{2}+11x=126$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+11x}{-2}=\frac{126}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{11}{-2}x=\frac{126}{-2}$$

11 ni -2 ga bo'lish.

$$x^{2}-\frac{11}{2}x=\frac{126}{-2}$$

126 ni -2 ga bo'lish.

$$x^{2}-\frac{11}{2}x=-63$$

-\frac{11}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{11}{4} olish uchun. Keyin, -\frac{11}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{11}{2}x+\left(-\frac{11}{4}\right)^{2}=-63+\left(-\frac{11}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{4} kvadratini chiqarish.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=-63+\frac{121}{16}$$

-63 ni \frac{121}{16} ga qo'shish.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=-\frac{887}{16}$$

x^{2}-\frac{11}{2}x+\frac{121}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{11}{4}\right)^{2}=-\frac{887}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{11}{4}\right)^{2}}=\sqrt{-\frac{887}{16}}$$

Qisqartirish.

$$x-\frac{11}{4}=\frac{\sqrt{887}i}{4} x-\frac{11}{4}=-\frac{\sqrt{887}i}{4}$$

\frac{11}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{11+\sqrt{887}i}{4} x=\frac{-\sqrt{887}i+11}{4}$$