930=(x+1)(x+2) eching

$$930 = ( x + 1 ) ( x + 2 )$$

x uchun yechish

$$x=-32$$

$$x=29$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+1 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$930=x^{2}+3x+2$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+3x+2=930$$

Ikkala tarafdan 930 ni ayirish.

$$x^{2}+3x+2-930=0$$

-928 olish uchun 2 dan 930 ni ayirish.

$$x^{2}+3x-928=0$$

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 -928 ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-928\right)}}{2}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\left(-928\right)}}{2}$$

-4 ni -928 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+3712}}{2}$$

9 ni 3712 ga qo'shish.

$$x=\frac{-3±\sqrt{3721}}{2}$$

3721 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±61}{2}$$

x=\frac{-3±61}{2} tenglamasini yeching, bunda ± musbat. -3 ni 61 ga qo'shish.

$$x=\frac{58}{2}$$

58 ni 2 ga bo'lish.

$$x=29$$

x=\frac{-3±61}{2} tenglamasini yeching, bunda ± manfiy. -3 dan 61 ni ayirish.

$$x=-\frac{64}{2}$$

-64 ni 2 ga bo'lish.

$$x=-32$$

Tenglama yechildi.

$$x=29 x=-32$$

Kvadratni yakunlash bo'yicha qadamlar

x+1 ga x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$930=x^{2}+3x+2$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+3x+2=930$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}+3x=930-2$$

928 olish uchun 930 dan 2 ni ayirish.

$$x^{2}+3x=928$$

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.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=928+\left(\frac{3}{2}\right)^{2}$$

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

$$x^{2}+3x+\frac{9}{4}=928+\frac{9}{4}$$

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

$$x^{2}+3x+\frac{9}{4}=\frac{3721}{4}$$

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.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{3721}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{3721}{4}}$$

Qisqartirish.

$$x+\frac{3}{2}=\frac{61}{2} x+\frac{3}{2}=-\frac{61}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$x=29 x=-32$$