-2/j+7=j/5 eching

$$\frac { - 2 } { j + 7 } = \frac { j } { 5 }$$

j uchun yechish

$$j=-5$$

$$j=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

j qiymati -7 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5\left(j+7\right) ga, j+7,5 ning eng kichik karralisiga ko‘paytiring.

$$5\left(-2\right)=\left(j+7\right)j$$

-10 hosil qilish uchun 5 va -2 ni ko'paytirish.

$$-10=\left(j+7\right)j$$

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

$$-10=j^{2}+7j$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$j^{2}+7j=-10$$

10 ni ikki tarafga qo’shing.

$$j^{2}+7j+10=0$$

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 10 ni c bilan almashtiring.

$$j=\frac{-7±\sqrt{7^{2}-4\times 10}}{2}$$

7 kvadratini chiqarish.

$$j=\frac{-7±\sqrt{49-4\times 10}}{2}$$

-4 ni 10 marotabaga ko'paytirish.

$$j=\frac{-7±\sqrt{49-40}}{2}$$

49 ni -40 ga qo'shish.

$$j=\frac{-7±\sqrt{9}}{2}$$

9 ning kvadrat ildizini chiqarish.

$$j=\frac{-7±3}{2}$$

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

$$j=-\frac{4}{2}$$

-4 ni 2 ga bo'lish.

$$j=-2$$

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

$$j=-\frac{10}{2}$$

-10 ni 2 ga bo'lish.

$$j=-5$$

Tenglama yechildi.

$$j=-2 j=-5$$

Kvadratni yakunlash bo'yicha qadamlar

j qiymati -7 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5\left(j+7\right) ga, j+7,5 ning eng kichik karralisiga ko‘paytiring.

$$5\left(-2\right)=\left(j+7\right)j$$

-10 hosil qilish uchun 5 va -2 ni ko'paytirish.

$$-10=\left(j+7\right)j$$

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

$$-10=j^{2}+7j$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$j^{2}+7j=-10$$

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.

$$j^{2}+7j+\left(\frac{7}{2}\right)^{2}=-10+\left(\frac{7}{2}\right)^{2}$$

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

$$j^{2}+7j+\frac{49}{4}=-10+\frac{49}{4}$$

-10 ni \frac{49}{4} ga qo'shish.

$$j^{2}+7j+\frac{49}{4}=\frac{9}{4}$$

j^{2}+7j+\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.

$$\left(j+\frac{7}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(j+\frac{7}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$j+\frac{7}{2}=\frac{3}{2} j+\frac{7}{2}=-\frac{3}{2}$$

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

$$j=-2 j=-5$$