6x(x+1)=5-x eching

$$6 x ( x + 1 ) = 5 - x$$

x uchun yechish

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1,666666667$$

$$x=\frac{1}{2}=0,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

6x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}+6x=5-x$$

Ikkala tarafdan 5 ni ayirish.

$$6x^{2}+6x-5=-x$$

x ni ikki tarafga qo’shing.

$$6x^{2}+6x-5+x=0$$

7x ni olish uchun 6x va x ni birlashtirish.

$$6x^{2}+7x-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 7 ni b va -5 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\times 6\left(-5\right)}}{2\times 6}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\times 6\left(-5\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49-24\left(-5\right)}}{2\times 6}$$

-24 ni -5 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+120}}{2\times 6}$$

49 ni 120 ga qo'shish.

$$x=\frac{-7±\sqrt{169}}{2\times 6}$$

169 ning kvadrat ildizini chiqarish.

$$x=\frac{-7±13}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{-7±13}{12}$$

x=\frac{-7±13}{12} tenglamasini yeching, bunda ± musbat. -7 ni 13 ga qo'shish.

$$x=\frac{6}{12}$$

\frac{6}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2}$$

x=\frac{-7±13}{12} tenglamasini yeching, bunda ± manfiy. -7 dan 13 ni ayirish.

$$x=-\frac{20}{12}$$

\frac{-20}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{5}{3}$$

Tenglama yechildi.

$$x=\frac{1}{2} x=-\frac{5}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

6x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}+6x=5-x$$

x ni ikki tarafga qo’shing.

$$6x^{2}+6x+x=5$$

7x ni olish uchun 6x va x ni birlashtirish.

$$6x^{2}+7x=5$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}+7x}{6}=\frac{5}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{7}{6}x=\frac{5}{6}$$

\frac{7}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{12} olish uchun. Keyin, \frac{7}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{7}{6}x+\left(\frac{7}{12}\right)^{2}=\frac{5}{6}+\left(\frac{7}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{12} kvadratini chiqarish.

$$x^{2}+\frac{7}{6}x+\frac{49}{144}=\frac{5}{6}+\frac{49}{144}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5}{6} ni \frac{49}{144} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{7}{6}x+\frac{49}{144}=\frac{169}{144}$$

x^{2}+\frac{7}{6}x+\frac{49}{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.

$$\left(x+\frac{7}{12}\right)^{2}=\frac{169}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{12}\right)^{2}}=\sqrt{\frac{169}{144}}$$

Qisqartirish.

$$x+\frac{7}{12}=\frac{13}{12} x+\frac{7}{12}=-\frac{13}{12}$$

Tenglamaning ikkala tarafidan \frac{7}{12} ni ayirish.

$$x=\frac{1}{2} x=-\frac{5}{3}$$