(2x-3)(2x+1)=5 eching

$$(2x-3)(2x+1)=5$$

x uchun yechish

$$x=-1$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x-3 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4x^{2}-4x-3=5$$

Ikkala tarafdan 5 ni ayirish.

$$4x^{2}-4x-3-5=0$$

-8 olish uchun -3 dan 5 ni ayirish.

$$4x^{2}-4x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -4 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 4\left(-8\right)}}{2\times 4}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 4\left(-8\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-16\left(-8\right)}}{2\times 4}$$

-16 ni -8 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+128}}{2\times 4}$$

16 ni 128 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{144}}{2\times 4}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±12}{2\times 4}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±12}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{4±12}{8}$$

x=\frac{4±12}{8} tenglamasini yeching, bunda ± musbat. 4 ni 12 ga qo'shish.

$$x=\frac{16}{8}$$

16 ni 8 ga bo'lish.

$$x=2$$

x=\frac{4±12}{8} tenglamasini yeching, bunda ± manfiy. 4 dan 12 ni ayirish.

$$x=-\frac{8}{8}$$

-8 ni 8 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=2 x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

2x-3 ga 2x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4x^{2}-4x-3=5$$

3 ni ikki tarafga qo’shing.

$$4x^{2}-4x=5+3$$

8 olish uchun 5 va 3'ni qo'shing.

$$4x^{2}-4x=8$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-4x}{4}=\frac{8}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{4}{4}\right)x=\frac{8}{4}$$

-4 ni 4 ga bo'lish.

$$x^{2}-x=\frac{8}{4}$$

8 ni 4 ga bo'lish.

$$x^{2}-x=2$$

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=2+\frac{1}{4}$$

2 ni \frac{1}{4} ga qo'shish.

$$x^{2}-x+\frac{1}{4}=\frac{9}{4}$$

x^{2}-x+\frac{1}{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.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{3}{2} x-\frac{1}{2}=-\frac{3}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=2 x=-1$$