x(x+7)/2=34 eching

$$\frac { x ( x + 7 ) } { 2 } = 34$$

x uchun yechish

$$x = \frac{\sqrt{321} - 7}{2} \approx 5,458236434$$

$$x=\frac{-\sqrt{321}-7}{2}\approx -12,458236434$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafini 2 ga ko‘paytiring.

$$x\left(x+7\right)=34\times 2$$

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

$$x^{2}+7x=34\times 2$$

68 hosil qilish uchun 34 va 2 ni ko'paytirish.

$$x^{2}+7x=68$$

Ikkala tarafdan 68 ni ayirish.

$$x^{2}+7x-68=0$$

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 -68 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-68\right)}}{2}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\left(-68\right)}}{2}$$

-4 ni -68 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+272}}{2}$$

49 ni 272 ga qo'shish.

$$x=\frac{-7±\sqrt{321}}{2}$$

x=\frac{-7±\sqrt{321}}{2} tenglamasini yeching, bunda ± musbat. -7 ni \sqrt{321} ga qo'shish.

$$x=\frac{\sqrt{321}-7}{2}$$

x=\frac{-7±\sqrt{321}}{2} tenglamasini yeching, bunda ± manfiy. -7 dan \sqrt{321} ni ayirish.

$$x=\frac{-\sqrt{321}-7}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{321}-7}{2} x=\frac{-\sqrt{321}-7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafini 2 ga ko‘paytiring.

$$x\left(x+7\right)=34\times 2$$

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

$$x^{2}+7x=34\times 2$$

68 hosil qilish uchun 34 va 2 ni ko'paytirish.

$$x^{2}+7x=68$$

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.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=68+\left(\frac{7}{2}\right)^{2}$$

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

$$x^{2}+7x+\frac{49}{4}=68+\frac{49}{4}$$

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

$$x^{2}+7x+\frac{49}{4}=\frac{321}{4}$$

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.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{321}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{321}{4}}$$

Qisqartirish.

$$x+\frac{7}{2}=\frac{\sqrt{321}}{2} x+\frac{7}{2}=-\frac{\sqrt{321}}{2}$$

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

$$x=\frac{\sqrt{321}-7}{2} x=\frac{-\sqrt{321}-7}{2}$$