1/2[x+(x+14)](x-05)=405 eching

$$\frac { 1 } { 2 } [ x + ( x + 14 ) ] ( x - 05 ) = 405$$

x uchun yechish

$$x = \frac{\sqrt{1669} - 7}{2} \approx 16,926698216$$

$$x=\frac{-\sqrt{1669}-7}{2}\approx -23,926698216$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ni olish uchun x va x ni birlashtirish.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\times 5\right)=405$$

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\right)=405$$

\frac{1}{2} ga 2x+14 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x+7\right)\left(x-0\right)=405$$

x+7 ga x-0 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x\left(x-0\right)+7\left(x-0\right)=405$$

Ikkala tarafdan 405 ni ayirish.

$$x\left(x-0\right)+7\left(x-0\right)-405=0$$

Shartlarni qayta saralash.

$$xx+7x-405=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+7x-405=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 7 ni b va -405 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-405\right)}}{2}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\left(-405\right)}}{2}$$

-4 ni -405 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+1620}}{2}$$

49 ni 1620 ga qo'shish.

$$x=\frac{-7±\sqrt{1669}}{2}$$

x=\frac{-7±\sqrt{1669}}{2} tenglamasini yeching, bunda ± musbat. -7 ni \sqrt{1669} ga qo'shish.

$$x=\frac{\sqrt{1669}-7}{2}$$

x=\frac{-7±\sqrt{1669}}{2} tenglamasini yeching, bunda ± manfiy. -7 dan \sqrt{1669} ni ayirish.

$$x=\frac{-\sqrt{1669}-7}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{1669}-7}{2} x=\frac{-\sqrt{1669}-7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x ni olish uchun x va x ni birlashtirish.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\times 5\right)=405$$

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\right)=405$$

\frac{1}{2} ga 2x+14 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x+7\right)\left(x-0\right)=405$$

x+7 ga x-0 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x\left(x-0\right)+7\left(x-0\right)=405$$

Shartlarni qayta saralash.

$$xx+7x=405$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+7x=405$$

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

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=405+\left(\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{2} kvadratini chiqarish.

$$x^{2}+7x+\frac{49}{4}=405+\frac{49}{4}$$

405 ni \frac{49}{4} ga qo'shish.

$$x^{2}+7x+\frac{49}{4}=\frac{1669}{4}$$

x^{2}+7x+\frac{49}{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.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{1669}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{1669}{4}}$$

Qisqartirish.

$$x+\frac{7}{2}=\frac{\sqrt{1669}}{2} x+\frac{7}{2}=-\frac{\sqrt{1669}}{2}$$

Tenglamaning ikkala tarafidan \frac{7}{2} ni ayirish.

$$x=\frac{\sqrt{1669}-7}{2} x=\frac{-\sqrt{1669}-7}{2}$$