(3x-9)x=5670 eching

$$( 3 x - 9 ) x = 5670$$

x uchun yechish

$$x=-42$$

$$x=45$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x-9 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-9x=5670$$

Ikkala tarafdan 5670 ni ayirish.

$$3x^{2}-9x-5670=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -9 ni b va -5670 ni c bilan almashtiring.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 3\left(-5670\right)}}{2\times 3}$$

-9 kvadratini chiqarish.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 3\left(-5670\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81-12\left(-5670\right)}}{2\times 3}$$

-12 ni -5670 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81+68040}}{2\times 3}$$

81 ni 68040 ga qo'shish.

$$x=\frac{-\left(-9\right)±\sqrt{68121}}{2\times 3}$$

68121 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±261}{2\times 3}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±261}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{9±261}{6}$$

x=\frac{9±261}{6} tenglamasini yeching, bunda ± musbat. 9 ni 261 ga qo'shish.

$$x=\frac{270}{6}$$

270 ni 6 ga bo'lish.

$$x=45$$

x=\frac{9±261}{6} tenglamasini yeching, bunda ± manfiy. 9 dan 261 ni ayirish.

$$x=-\frac{252}{6}$$

-252 ni 6 ga bo'lish.

$$x=-42$$

Tenglama yechildi.

$$x=45 x=-42$$

Kvadratni yakunlash bo'yicha qadamlar

3x-9 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-9x=5670$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-9x}{3}=\frac{5670}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{9}{3}\right)x=\frac{5670}{3}$$

-9 ni 3 ga bo'lish.

$$x^{2}-3x=\frac{5670}{3}$$

5670 ni 3 ga bo'lish.

$$x^{2}-3x=1890$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=1890+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=1890+\frac{9}{4}$$

1890 ni \frac{9}{4} ga qo'shish.

$$x^{2}-3x+\frac{9}{4}=\frac{7569}{4}$$

x^{2}-3x+\frac{9}{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.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{7569}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{7569}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{87}{2} x-\frac{3}{2}=-\frac{87}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=45 x=-42$$