(x+7)x=13*2 eching

$$( x + 7 ) x = 13 \cdot 2$$

x uchun yechish

$$x = \frac{3 \sqrt{17} - 7}{2} \approx 2,684658438$$

$$x=\frac{-3\sqrt{17}-7}{2}\approx -9,684658438$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+7 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+7x=13\times 2$$

26 hosil qilish uchun 13 va 2 ni ko'paytirish.

$$x^{2}+7x=26$$

Ikkala tarafdan 26 ni ayirish.

$$x^{2}+7x-26=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 7 ni b va -26 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-26\right)}}{2}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\left(-26\right)}}{2}$$

-4 ni -26 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+104}}{2}$$

49 ni 104 ga qo'shish.

$$x=\frac{-7±\sqrt{153}}{2}$$

153 ning kvadrat ildizini chiqarish.

$$x=\frac{-7±3\sqrt{17}}{2}$$

x=\frac{-7±3\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. -7 ni 3\sqrt{17} ga qo'shish.

$$x=\frac{3\sqrt{17}-7}{2}$$

x=\frac{-7±3\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. -7 dan 3\sqrt{17} ni ayirish.

$$x=\frac{-3\sqrt{17}-7}{2}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{17}-7}{2} x=\frac{-3\sqrt{17}-7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x+7 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+7x=13\times 2$$

26 hosil qilish uchun 13 va 2 ni ko'paytirish.

$$x^{2}+7x=26$$

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.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=26+\left(\frac{7}{2}\right)^{2}$$

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

$$x^{2}+7x+\frac{49}{4}=26+\frac{49}{4}$$

26 ni \frac{49}{4} ga qo'shish.

$$x^{2}+7x+\frac{49}{4}=\frac{153}{4}$$

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.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{153}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{153}{4}}$$

Qisqartirish.

$$x+\frac{7}{2}=\frac{3\sqrt{17}}{2} x+\frac{7}{2}=-\frac{3\sqrt{17}}{2}$$

Tenglamaning ikkala tarafidan \frac{7}{2} ni ayirish.

$$x=\frac{3\sqrt{17}-7}{2} x=\frac{-3\sqrt{17}-7}{2}$$