(x)(x+2)=624 eching

$$( x ) ( x + 2 ) = 624$$

x uchun yechish

$$x=-26$$

$$x=24$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+2x=624$$

Ikkala tarafdan 624 ni ayirish.

$$x^{2}+2x-624=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va -624 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-624\right)}}{2}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\left(-624\right)}}{2}$$

-4 ni -624 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+2496}}{2}$$

4 ni 2496 ga qo'shish.

$$x=\frac{-2±\sqrt{2500}}{2}$$

2500 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±50}{2}$$

x=\frac{-2±50}{2} tenglamasini yeching, bunda ± musbat. -2 ni 50 ga qo'shish.

$$x=\frac{48}{2}$$

48 ni 2 ga bo'lish.

$$x=24$$

x=\frac{-2±50}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 50 ni ayirish.

$$x=-\frac{52}{2}$$

-52 ni 2 ga bo'lish.

$$x=-26$$

Tenglama yechildi.

$$x=24 x=-26$$

Kvadratni yakunlash bo'yicha qadamlar

x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+2x=624$$

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=624+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=624+1$$

624 ni 1 ga qo'shish.

$$x^{2}+2x+1=625$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=625$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{625}$$

Qisqartirish.

$$x+1=25 x+1=-25$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=24 x=-26$$