(6x-1)(2x+7)=(4-5x)(1-6x) eching

$$(6x-1)(2x+7)=(4-5x)(1-6x)$$

x uchun yechish

$$x=\frac{1}{6}\approx 0,166666667$$

$$x = \frac{11}{3} = 3\frac{2}{3} \approx 3,666666667$$

Kvadrat tenglamalaridan foydalanish qoidalari

6x-1 ga 2x+7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}+40x-7=\left(4-5x\right)\left(1-6x\right)$$

4-5x ga 1-6x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}+40x-7=4-29x+30x^{2}$$

Ikkala tarafdan 4 ni ayirish.

$$12x^{2}+40x-7-4=-29x+30x^{2}$$

-11 olish uchun -7 dan 4 ni ayirish.

$$12x^{2}+40x-11=-29x+30x^{2}$$

29x ni ikki tarafga qo’shing.

$$12x^{2}+40x-11+29x=30x^{2}$$

69x ni olish uchun 40x va 29x ni birlashtirish.

$$12x^{2}+69x-11=30x^{2}$$

Ikkala tarafdan 30x^{2} ni ayirish.

$$12x^{2}+69x-11-30x^{2}=0$$

-18x^{2} ni olish uchun 12x^{2} va -30x^{2} ni birlashtirish.

$$-18x^{2}+69x-11=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -18 ni a, 69 ni b va -11 ni c bilan almashtiring.

$$x=\frac{-69±\sqrt{69^{2}-4\left(-18\right)\left(-11\right)}}{2\left(-18\right)}$$

69 kvadratini chiqarish.

$$x=\frac{-69±\sqrt{4761-4\left(-18\right)\left(-11\right)}}{2\left(-18\right)}$$

-4 ni -18 marotabaga ko'paytirish.

$$x=\frac{-69±\sqrt{4761+72\left(-11\right)}}{2\left(-18\right)}$$

72 ni -11 marotabaga ko'paytirish.

$$x=\frac{-69±\sqrt{4761-792}}{2\left(-18\right)}$$

4761 ni -792 ga qo'shish.

$$x=\frac{-69±\sqrt{3969}}{2\left(-18\right)}$$

3969 ning kvadrat ildizini chiqarish.

$$x=\frac{-69±63}{2\left(-18\right)}$$

2 ni -18 marotabaga ko'paytirish.

$$x=\frac{-69±63}{-36}$$

x=\frac{-69±63}{-36} tenglamasini yeching, bunda ± musbat. -69 ni 63 ga qo'shish.

$$x=-\frac{6}{-36}$$

\frac{-6}{-36} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{6}$$

x=\frac{-69±63}{-36} tenglamasini yeching, bunda ± manfiy. -69 dan 63 ni ayirish.

$$x=-\frac{132}{-36}$$

\frac{-132}{-36} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{11}{3}$$

Tenglama yechildi.

$$x=\frac{1}{6} x=\frac{11}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

6x-1 ga 2x+7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}+40x-7=\left(4-5x\right)\left(1-6x\right)$$

4-5x ga 1-6x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}+40x-7=4-29x+30x^{2}$$

29x ni ikki tarafga qo’shing.

$$12x^{2}+40x-7+29x=4+30x^{2}$$

69x ni olish uchun 40x va 29x ni birlashtirish.

$$12x^{2}+69x-7=4+30x^{2}$$

Ikkala tarafdan 30x^{2} ni ayirish.

$$12x^{2}+69x-7-30x^{2}=4$$

-18x^{2} ni olish uchun 12x^{2} va -30x^{2} ni birlashtirish.

$$-18x^{2}+69x-7=4$$

7 ni ikki tarafga qo’shing.

$$-18x^{2}+69x=4+7$$

11 olish uchun 4 va 7'ni qo'shing.

$$-18x^{2}+69x=11$$

Ikki tarafini -18 ga bo‘ling.

$$\frac{-18x^{2}+69x}{-18}=\frac{11}{-18}$$

-18 ga bo'lish -18 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{69}{-18}x=\frac{11}{-18}$$

\frac{69}{-18} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{23}{6}x=\frac{11}{-18}$$

11 ni -18 ga bo'lish.

$$x^{2}-\frac{23}{6}x=-\frac{11}{18}$$

-\frac{23}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{23}{12} olish uchun. Keyin, -\frac{23}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{23}{6}x+\left(-\frac{23}{12}\right)^{2}=-\frac{11}{18}+\left(-\frac{23}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{23}{12} kvadratini chiqarish.

$$x^{2}-\frac{23}{6}x+\frac{529}{144}=-\frac{11}{18}+\frac{529}{144}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{11}{18} ni \frac{529}{144} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{23}{6}x+\frac{529}{144}=\frac{49}{16}$$

x^{2}-\frac{23}{6}x+\frac{529}{144} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{23}{12}\right)^{2}=\frac{49}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{23}{12}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Qisqartirish.

$$x-\frac{23}{12}=\frac{7}{4} x-\frac{23}{12}=-\frac{7}{4}$$

\frac{23}{12} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{11}{3} x=\frac{1}{6}$$