-(3x-4)4(x-5)=2(7-4x) eching

$$-(3x-4)4(x-5)=2(7-4x)$$

x uchun yechish

$$x=\frac{\sqrt{159}}{6}+\frac{7}{2}\approx 5,601586702$$

$$x=-\frac{\sqrt{159}}{6}+\frac{7}{2}\approx 1,398413298$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x-4 teskarisini topish uchun har birining teskarisini toping.

$$\left(-3x-\left(-4\right)\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

-4 ning teskarisi 4 ga teng.

$$\left(-3x+4\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

-3x+4 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-12x+16\right)\left(x-5\right)=2\left(7-4x\right)$$

-12x+16 ifodaning har bir elementini x-5 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$-12x^{2}+60x+16x-80=2\left(7-4x\right)$$

76x ni olish uchun 60x va 16x ni birlashtirish.

$$-12x^{2}+76x-80=2\left(7-4x\right)$$

2 ga 7-4x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-12x^{2}+76x-80=14-8x$$

Ikkala tarafdan 14 ni ayirish.

$$-12x^{2}+76x-80-14=-8x$$

-94 olish uchun -80 dan 14 ni ayirish.

$$-12x^{2}+76x-94=-8x$$

8x ni ikki tarafga qo’shing.

$$-12x^{2}+76x-94+8x=0$$

84x ni olish uchun 76x va 8x ni birlashtirish.

$$-12x^{2}+84x-94=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -12 ni a, 84 ni b va -94 ni c bilan almashtiring.

$$x=\frac{-84±\sqrt{84^{2}-4\left(-12\right)\left(-94\right)}}{2\left(-12\right)}$$

84 kvadratini chiqarish.

$$x=\frac{-84±\sqrt{7056-4\left(-12\right)\left(-94\right)}}{2\left(-12\right)}$$

-4 ni -12 marotabaga ko'paytirish.

$$x=\frac{-84±\sqrt{7056+48\left(-94\right)}}{2\left(-12\right)}$$

48 ni -94 marotabaga ko'paytirish.

$$x=\frac{-84±\sqrt{7056-4512}}{2\left(-12\right)}$$

7056 ni -4512 ga qo'shish.

$$x=\frac{-84±\sqrt{2544}}{2\left(-12\right)}$$

2544 ning kvadrat ildizini chiqarish.

$$x=\frac{-84±4\sqrt{159}}{2\left(-12\right)}$$

2 ni -12 marotabaga ko'paytirish.

$$x=\frac{-84±4\sqrt{159}}{-24}$$

x=\frac{-84±4\sqrt{159}}{-24} tenglamasini yeching, bunda ± musbat. -84 ni 4\sqrt{159} ga qo'shish.

$$x=\frac{4\sqrt{159}-84}{-24}$$

-84+4\sqrt{159} ni -24 ga bo'lish.

$$x=-\frac{\sqrt{159}}{6}+\frac{7}{2}$$

x=\frac{-84±4\sqrt{159}}{-24} tenglamasini yeching, bunda ± manfiy. -84 dan 4\sqrt{159} ni ayirish.

$$x=\frac{-4\sqrt{159}-84}{-24}$$

-84-4\sqrt{159} ni -24 ga bo'lish.

$$x=\frac{\sqrt{159}}{6}+\frac{7}{2}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{159}}{6}+\frac{7}{2} x=\frac{\sqrt{159}}{6}+\frac{7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

3x-4 teskarisini topish uchun har birining teskarisini toping.

$$\left(-3x-\left(-4\right)\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

-4 ning teskarisi 4 ga teng.

$$\left(-3x+4\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

-3x+4 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-12x+16\right)\left(x-5\right)=2\left(7-4x\right)$$

-12x+16 ifodaning har bir elementini x-5 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$-12x^{2}+60x+16x-80=2\left(7-4x\right)$$

76x ni olish uchun 60x va 16x ni birlashtirish.

$$-12x^{2}+76x-80=2\left(7-4x\right)$$

2 ga 7-4x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-12x^{2}+76x-80=14-8x$$

8x ni ikki tarafga qo’shing.

$$-12x^{2}+76x-80+8x=14$$

84x ni olish uchun 76x va 8x ni birlashtirish.

$$-12x^{2}+84x-80=14$$

80 ni ikki tarafga qo’shing.

$$-12x^{2}+84x=14+80$$

94 olish uchun 14 va 80'ni qo'shing.

$$-12x^{2}+84x=94$$

Ikki tarafini -12 ga bo‘ling.

$$\frac{-12x^{2}+84x}{-12}=\frac{94}{-12}$$

-12 ga bo'lish -12 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{84}{-12}x=\frac{94}{-12}$$

84 ni -12 ga bo'lish.

$$x^{2}-7x=\frac{94}{-12}$$

\frac{94}{-12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-7x=-\frac{47}{6}$$

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

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-\frac{47}{6}+\left(-\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$x^{2}-7x+\frac{49}{4}=-\frac{47}{6}+\frac{49}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{47}{6} ni \frac{49}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-7x+\frac{49}{4}=\frac{53}{12}$$

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

$$\left(x-\frac{7}{2}\right)^{2}=\frac{53}{12}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{53}{12}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{\sqrt{159}}{6} x-\frac{7}{2}=-\frac{\sqrt{159}}{6}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{159}}{6}+\frac{7}{2} x=-\frac{\sqrt{159}}{6}+\frac{7}{2}$$