6/2x+4=x-5/10 eching

$$\frac { 6 } { 2 x + 4 } = \frac { x - 5 } { 10 }$$

x uchun yechish

$$x=-5$$

$$x=8$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 10\left(x+2\right) ga, 2x+4,10 ning eng kichik karralisiga ko‘paytiring.

$$5\times 6=\left(x+2\right)\left(x-5\right)$$

30 hosil qilish uchun 5 va 6 ni ko'paytirish.

$$30=\left(x+2\right)\left(x-5\right)$$

x+2 ga x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$30=x^{2}-3x-10$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x-10=30$$

Ikkala tarafdan 30 ni ayirish.

$$x^{2}-3x-10-30=0$$

-40 olish uchun -10 dan 30 ni ayirish.

$$x^{2}-3x-40=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va -40 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-40\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-40\right)}}{2}$$

-4 ni -40 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+160}}{2}$$

9 ni 160 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{169}}{2}$$

169 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±13}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±13}{2}$$

x=\frac{3±13}{2} tenglamasini yeching, bunda ± musbat. 3 ni 13 ga qo'shish.

$$x=\frac{16}{2}$$

16 ni 2 ga bo'lish.

$$x=8$$

x=\frac{3±13}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 13 ni ayirish.

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

-10 ni 2 ga bo'lish.

$$x=-5$$

Tenglama yechildi.

$$x=8 x=-5$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 10\left(x+2\right) ga, 2x+4,10 ning eng kichik karralisiga ko‘paytiring.

$$5\times 6=\left(x+2\right)\left(x-5\right)$$

30 hosil qilish uchun 5 va 6 ni ko'paytirish.

$$30=\left(x+2\right)\left(x-5\right)$$

x+2 ga x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$30=x^{2}-3x-10$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-3x-10=30$$

10 ni ikki tarafga qo’shing.

$$x^{2}-3x=30+10$$

40 olish uchun 30 va 10'ni qo'shing.

$$x^{2}-3x=40$$

-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.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=40+\left(-\frac{3}{2}\right)^{2}$$

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

$$x^{2}-3x+\frac{9}{4}=40+\frac{9}{4}$$

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

$$x^{2}-3x+\frac{9}{4}=\frac{169}{4}$$

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.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{169}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{169}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{13}{2} x-\frac{3}{2}=-\frac{13}{2}$$

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

$$x=8 x=-5$$