96=left(x+15right)left(x+5right) eching

$$96 = \left( x+15 \right) \left( x+5 \right)$$

x uchun yechish

$$x=-21$$

$$x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+15 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$96=x^{2}+20x+75$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+20x+75=96$$

Ikkala tarafdan 96 ni ayirish.

$$x^{2}+20x+75-96=0$$

-21 olish uchun 75 dan 96 ni ayirish.

$$x^{2}+20x-21=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 20 ni b va -21 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-21\right)}}{2}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\left(-21\right)}}{2}$$

-4 ni -21 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+84}}{2}$$

400 ni 84 ga qo'shish.

$$x=\frac{-20±\sqrt{484}}{2}$$

484 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±22}{2}$$

x=\frac{-20±22}{2} tenglamasini yeching, bunda ± musbat. -20 ni 22 ga qo'shish.

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

2 ni 2 ga bo'lish.

$$x=1$$

x=\frac{-20±22}{2} tenglamasini yeching, bunda ± manfiy. -20 dan 22 ni ayirish.

$$x=-\frac{42}{2}$$

-42 ni 2 ga bo'lish.

$$x=-21$$

Tenglama yechildi.

$$x=1 x=-21$$

Kvadratni yakunlash bo'yicha qadamlar

x+15 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$96=x^{2}+20x+75$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+20x+75=96$$

Ikkala tarafdan 75 ni ayirish.

$$x^{2}+20x=96-75$$

21 olish uchun 96 dan 75 ni ayirish.

$$x^{2}+20x=21$$

20 ni bo‘lish, x shartining koeffitsienti, 2 ga 10 olish uchun. Keyin, 10 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+20x+10^{2}=21+10^{2}$$

10 kvadratini chiqarish.

$$x^{2}+20x+100=21+100$$

21 ni 100 ga qo'shish.

$$x^{2}+20x+100=121$$

x^{2}+20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+10\right)^{2}=121$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{121}$$

Qisqartirish.

$$x+10=11 x+10=-11$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$x=1 x=-21$$