(25-2x+1)x=80 eching

$$(25-2x+1)x=80$$

x uchun yechish

$$x=5$$

$$x=8$$

Kvadrat tenglamalaridan foydalanish qoidalari

26 olish uchun 25 va 1'ni qo'shing.

$$\left(26-2x\right)x=80$$

26-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$26x-2x^{2}=80$$

Ikkala tarafdan 80 ni ayirish.

$$26x-2x^{2}-80=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-2x^{2}+26x-80=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 26 ni b va -80 ni c bilan almashtiring.

$$x=\frac{-26±\sqrt{26^{2}-4\left(-2\right)\left(-80\right)}}{2\left(-2\right)}$$

26 kvadratini chiqarish.

$$x=\frac{-26±\sqrt{676-4\left(-2\right)\left(-80\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-26±\sqrt{676+8\left(-80\right)}}{2\left(-2\right)}$$

8 ni -80 marotabaga ko'paytirish.

$$x=\frac{-26±\sqrt{676-640}}{2\left(-2\right)}$$

676 ni -640 ga qo'shish.

$$x=\frac{-26±\sqrt{36}}{2\left(-2\right)}$$

36 ning kvadrat ildizini chiqarish.

$$x=\frac{-26±6}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-26±6}{-4}$$

x=\frac{-26±6}{-4} tenglamasini yeching, bunda ± musbat. -26 ni 6 ga qo'shish.

$$x=-\frac{20}{-4}$$

-20 ni -4 ga bo'lish.

$$x=5$$

x=\frac{-26±6}{-4} tenglamasini yeching, bunda ± manfiy. -26 dan 6 ni ayirish.

$$x=-\frac{32}{-4}$$

-32 ni -4 ga bo'lish.

$$x=8$$

Tenglama yechildi.

$$x=5 x=8$$

Kvadratni yakunlash bo'yicha qadamlar

26 olish uchun 25 va 1'ni qo'shing.

$$\left(26-2x\right)x=80$$

26-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$26x-2x^{2}=80$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-2x^{2}+26x=80$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+26x}{-2}=\frac{80}{-2}$$

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

$$x^{2}+\frac{26}{-2}x=\frac{80}{-2}$$

26 ni -2 ga bo'lish.

$$x^{2}-13x=\frac{80}{-2}$$

80 ni -2 ga bo'lish.

$$x^{2}-13x=-40$$

-13 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{13}{2} olish uchun. Keyin, -\frac{13}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-13x+\left(-\frac{13}{2}\right)^{2}=-40+\left(-\frac{13}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{13}{2} kvadratini chiqarish.

$$x^{2}-13x+\frac{169}{4}=-40+\frac{169}{4}$$

-40 ni \frac{169}{4} ga qo'shish.

$$x^{2}-13x+\frac{169}{4}=\frac{9}{4}$$

x^{2}-13x+\frac{169}{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.

$$\left(x-\frac{13}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{13}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$x-\frac{13}{2}=\frac{3}{2} x-\frac{13}{2}=-\frac{3}{2}$$

\frac{13}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=8 x=5$$