15*(1-x)*(1+x)+7x-3=0 eching

$$15 \times (1-x) \times (1+x)+7x-3=0$$

x uchun yechish

$$x = \frac{\sqrt{769} + 7}{30} \approx 1,157694975$$

$$x=\frac{7-\sqrt{769}}{30}\approx -0,691028308$$

Kvadrat tenglamalaridan foydalanish qoidalari

15 ga 1-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(15-15x\right)\left(1+x\right)+7x-3=0$$

15-15x ga 1+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$15-15x^{2}+7x-3=0$$

12 olish uchun 15 dan 3 ni ayirish.

$$12-15x^{2}+7x=0$$

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.

$$-15x^{2}+7x+12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -15 ni a, 7 ni b va 12 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-15\right)\times 12}}{2\left(-15\right)}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\left(-15\right)\times 12}}{2\left(-15\right)}$$

-4 ni -15 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+60\times 12}}{2\left(-15\right)}$$

60 ni 12 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+720}}{2\left(-15\right)}$$

49 ni 720 ga qo'shish.

$$x=\frac{-7±\sqrt{769}}{2\left(-15\right)}$$

2 ni -15 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{769}}{-30}$$

x=\frac{-7±\sqrt{769}}{-30} tenglamasini yeching, bunda ± musbat. -7 ni \sqrt{769} ga qo'shish.

$$x=\frac{\sqrt{769}-7}{-30}$$

-7+\sqrt{769} ni -30 ga bo'lish.

$$x=\frac{7-\sqrt{769}}{30}$$

x=\frac{-7±\sqrt{769}}{-30} tenglamasini yeching, bunda ± manfiy. -7 dan \sqrt{769} ni ayirish.

$$x=\frac{-\sqrt{769}-7}{-30}$$

-7-\sqrt{769} ni -30 ga bo'lish.

$$x=\frac{\sqrt{769}+7}{30}$$

Tenglama yechildi.

$$x=\frac{7-\sqrt{769}}{30} x=\frac{\sqrt{769}+7}{30}$$

Kvadratni yakunlash bo'yicha qadamlar

15 ga 1-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(15-15x\right)\left(1+x\right)+7x-3=0$$

15-15x ga 1+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$15-15x^{2}+7x-3=0$$

12 olish uchun 15 dan 3 ni ayirish.

$$12-15x^{2}+7x=0$$

Ikkala tarafdan 12 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-15x^{2}+7x=-12$$

Ikki tarafini -15 ga bo‘ling.

$$\frac{-15x^{2}+7x}{-15}=-\frac{12}{-15}$$

-15 ga bo'lish -15 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{7}{-15}x=-\frac{12}{-15}$$

7 ni -15 ga bo'lish.

$$x^{2}-\frac{7}{15}x=-\frac{12}{-15}$$

\frac{-12}{-15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{7}{15}x=\frac{4}{5}$$

-\frac{7}{15} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{30} olish uchun. Keyin, -\frac{7}{30} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{7}{15}x+\left(-\frac{7}{30}\right)^{2}=\frac{4}{5}+\left(-\frac{7}{30}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{30} kvadratini chiqarish.

$$x^{2}-\frac{7}{15}x+\frac{49}{900}=\frac{4}{5}+\frac{49}{900}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{4}{5} ni \frac{49}{900} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{7}{15}x+\frac{49}{900}=\frac{769}{900}$$

x^{2}-\frac{7}{15}x+\frac{49}{900} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{7}{30}\right)^{2}=\frac{769}{900}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{30}\right)^{2}}=\sqrt{\frac{769}{900}}$$

Qisqartirish.

$$x-\frac{7}{30}=\frac{\sqrt{769}}{30} x-\frac{7}{30}=-\frac{\sqrt{769}}{30}$$

\frac{7}{30} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{769}+7}{30} x=\frac{7-\sqrt{769}}{30}$$