6(6+15)=x(x+5) eching

$$6(6+15)=x(x+5)$$

x uchun yechish

$$x=-14$$

$$x=9$$

Kvadrat tenglamalaridan foydalanish qoidalari

21 olish uchun 6 va 15'ni qo'shing.

$$6\times 21=x\left(x+5\right)$$

126 hosil qilish uchun 6 va 21 ni ko'paytirish.

$$126=x\left(x+5\right)$$

x ga x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$126=x^{2}+5x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+5x=126$$

Ikkala tarafdan 126 ni ayirish.

$$x^{2}+5x-126=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 5 ni b va -126 ni c bilan almashtiring.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-126\right)}}{2}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\left(-126\right)}}{2}$$

-4 ni -126 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+504}}{2}$$

25 ni 504 ga qo'shish.

$$x=\frac{-5±\sqrt{529}}{2}$$

529 ning kvadrat ildizini chiqarish.

$$x=\frac{-5±23}{2}$$

x=\frac{-5±23}{2} tenglamasini yeching, bunda ± musbat. -5 ni 23 ga qo'shish.

$$x=\frac{18}{2}$$

18 ni 2 ga bo'lish.

$$x=9$$

x=\frac{-5±23}{2} tenglamasini yeching, bunda ± manfiy. -5 dan 23 ni ayirish.

$$x=-\frac{28}{2}$$

-28 ni 2 ga bo'lish.

$$x=-14$$

Tenglama yechildi.

$$x=9 x=-14$$

Kvadratni yakunlash bo'yicha qadamlar

21 olish uchun 6 va 15'ni qo'shing.

$$6\times 21=x\left(x+5\right)$$

126 hosil qilish uchun 6 va 21 ni ko'paytirish.

$$126=x\left(x+5\right)$$

x ga x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$126=x^{2}+5x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+5x=126$$

5 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{2} olish uchun. Keyin, \frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=126+\left(\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{2} kvadratini chiqarish.

$$x^{2}+5x+\frac{25}{4}=126+\frac{25}{4}$$

126 ni \frac{25}{4} ga qo'shish.

$$x^{2}+5x+\frac{25}{4}=\frac{529}{4}$$

x^{2}+5x+\frac{25}{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.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{529}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{529}{4}}$$

Qisqartirish.

$$x+\frac{5}{2}=\frac{23}{2} x+\frac{5}{2}=-\frac{23}{2}$$

Tenglamaning ikkala tarafidan \frac{5}{2} ni ayirish.

$$x=9 x=-14$$