(2x+1)*(x+5)=8*5 eching

$$( 2 x + 1 ) \cdot ( x + 5 ) = 8 \cdot 5$$

x uchun yechish

$$x = \frac{\sqrt{401} - 11}{4} \approx 2,256246099$$

$$x=\frac{-\sqrt{401}-11}{4}\approx -7,756246099$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x+1 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+11x+5=8\times 5$$

40 hosil qilish uchun 8 va 5 ni ko'paytirish.

$$2x^{2}+11x+5=40$$

Ikkala tarafdan 40 ni ayirish.

$$2x^{2}+11x+5-40=0$$

-35 olish uchun 5 dan 40 ni ayirish.

$$2x^{2}+11x-35=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 11 ni b va -35 ni c bilan almashtiring.

$$x=\frac{-11±\sqrt{11^{2}-4\times 2\left(-35\right)}}{2\times 2}$$

11 kvadratini chiqarish.

$$x=\frac{-11±\sqrt{121-4\times 2\left(-35\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121-8\left(-35\right)}}{2\times 2}$$

-8 ni -35 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121+280}}{2\times 2}$$

121 ni 280 ga qo'shish.

$$x=\frac{-11±\sqrt{401}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{401}}{4}$$

x=\frac{-11±\sqrt{401}}{4} tenglamasini yeching, bunda ± musbat. -11 ni \sqrt{401} ga qo'shish.

$$x=\frac{\sqrt{401}-11}{4}$$

x=\frac{-11±\sqrt{401}}{4} tenglamasini yeching, bunda ± manfiy. -11 dan \sqrt{401} ni ayirish.

$$x=\frac{-\sqrt{401}-11}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{401}-11}{4} x=\frac{-\sqrt{401}-11}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

2x+1 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+11x+5=8\times 5$$

40 hosil qilish uchun 8 va 5 ni ko'paytirish.

$$2x^{2}+11x+5=40$$

Ikkala tarafdan 5 ni ayirish.

$$2x^{2}+11x=40-5$$

35 olish uchun 40 dan 5 ni ayirish.

$$2x^{2}+11x=35$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+11x}{2}=\frac{35}{2}$$

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

$$x^{2}+\frac{11}{2}x=\frac{35}{2}$$

\frac{11}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{11}{4} olish uchun. Keyin, \frac{11}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{11}{2}x+\left(\frac{11}{4}\right)^{2}=\frac{35}{2}+\left(\frac{11}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{11}{4} kvadratini chiqarish.

$$x^{2}+\frac{11}{2}x+\frac{121}{16}=\frac{35}{2}+\frac{121}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{35}{2} ni \frac{121}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{11}{2}x+\frac{121}{16}=\frac{401}{16}$$

x^{2}+\frac{11}{2}x+\frac{121}{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.

$$\left(x+\frac{11}{4}\right)^{2}=\frac{401}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{11}{4}\right)^{2}}=\sqrt{\frac{401}{16}}$$

Qisqartirish.

$$x+\frac{11}{4}=\frac{\sqrt{401}}{4} x+\frac{11}{4}=-\frac{\sqrt{401}}{4}$$

Tenglamaning ikkala tarafidan \frac{11}{4} ni ayirish.

$$x=\frac{\sqrt{401}-11}{4} x=\frac{-\sqrt{401}-11}{4}$$