left(2x-5right)left(x+3right)=15-6x eching

$$\left( 2x-5 \right) \left( x+3 \right) = 15-6x$$

x uchun yechish

$$x=-6$$

$$x = \frac{5}{2} = 2\frac{1}{2} = 2,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x-5 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+x-15=15-6x$$

Ikkala tarafdan 15 ni ayirish.

$$2x^{2}+x-15-15=-6x$$

-30 olish uchun -15 dan 15 ni ayirish.

$$2x^{2}+x-30=-6x$$

6x ni ikki tarafga qo’shing.

$$2x^{2}+x-30+6x=0$$

7x ni olish uchun x va 6x ni birlashtirish.

$$2x^{2}+7x-30=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 7 ni b va -30 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\times 2\left(-30\right)}}{2\times 2}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\times 2\left(-30\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49-8\left(-30\right)}}{2\times 2}$$

-8 ni -30 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+240}}{2\times 2}$$

49 ni 240 ga qo'shish.

$$x=\frac{-7±\sqrt{289}}{2\times 2}$$

289 ning kvadrat ildizini chiqarish.

$$x=\frac{-7±17}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-7±17}{4}$$

x=\frac{-7±17}{4} tenglamasini yeching, bunda ± musbat. -7 ni 17 ga qo'shish.

$$x=\frac{10}{4}$$

\frac{10}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{2}$$

x=\frac{-7±17}{4} tenglamasini yeching, bunda ± manfiy. -7 dan 17 ni ayirish.

$$x=-\frac{24}{4}$$

-24 ni 4 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=\frac{5}{2} x=-6$$

Kvadratni yakunlash bo'yicha qadamlar

2x-5 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+x-15=15-6x$$

6x ni ikki tarafga qo’shing.

$$2x^{2}+x-15+6x=15$$

7x ni olish uchun x va 6x ni birlashtirish.

$$2x^{2}+7x-15=15$$

15 ni ikki tarafga qo’shing.

$$2x^{2}+7x=15+15$$

30 olish uchun 15 va 15'ni qo'shing.

$$2x^{2}+7x=30$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+7x}{2}=\frac{30}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{7}{2}x=\frac{30}{2}$$

30 ni 2 ga bo'lish.

$$x^{2}+\frac{7}{2}x=15$$

\frac{7}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{4} olish uchun. Keyin, \frac{7}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{7}{2}x+\left(\frac{7}{4}\right)^{2}=15+\left(\frac{7}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{4} kvadratini chiqarish.

$$x^{2}+\frac{7}{2}x+\frac{49}{16}=15+\frac{49}{16}$$

15 ni \frac{49}{16} ga qo'shish.

$$x^{2}+\frac{7}{2}x+\frac{49}{16}=\frac{289}{16}$$

x^{2}+\frac{7}{2}x+\frac{49}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{7}{4}\right)^{2}=\frac{289}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{4}\right)^{2}}=\sqrt{\frac{289}{16}}$$

Qisqartirish.

$$x+\frac{7}{4}=\frac{17}{4} x+\frac{7}{4}=-\frac{17}{4}$$

Tenglamaning ikkala tarafidan \frac{7}{4} ni ayirish.

$$x=\frac{5}{2} x=-6$$