(32-2x)(20-x)=57 eching

$$( 32 - 2 x ) ( 20 - x ) = 57$$

x uchun yechish

$$x=\frac{\sqrt{130}}{2}+18\approx 23,700877125$$

$$x=-\frac{\sqrt{130}}{2}+18\approx 12,299122875$$

Kvadrat tenglamalaridan foydalanish qoidalari

32-2x ga 20-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$640-72x+2x^{2}=57$$

Ikkala tarafdan 57 ni ayirish.

$$640-72x+2x^{2}-57=0$$

583 olish uchun 640 dan 57 ni ayirish.

$$583-72x+2x^{2}=0$$

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.

$$2x^{2}-72x+583=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -72 ni b va 583 ni c bilan almashtiring.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 2\times 583}}{2\times 2}$$

-72 kvadratini chiqarish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4\times 2\times 583}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-8\times 583}}{2\times 2}$$

-8 ni 583 marotabaga ko'paytirish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4664}}{2\times 2}$$

5184 ni -4664 ga qo'shish.

$$x=\frac{-\left(-72\right)±\sqrt{520}}{2\times 2}$$

520 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-72\right)±2\sqrt{130}}{2\times 2}$$

-72 ning teskarisi 72 ga teng.

$$x=\frac{72±2\sqrt{130}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{72±2\sqrt{130}}{4}$$

x=\frac{72±2\sqrt{130}}{4} tenglamasini yeching, bunda ± musbat. 72 ni 2\sqrt{130} ga qo'shish.

$$x=\frac{2\sqrt{130}+72}{4}$$

72+2\sqrt{130} ni 4 ga bo'lish.

$$x=\frac{\sqrt{130}}{2}+18$$

x=\frac{72±2\sqrt{130}}{4} tenglamasini yeching, bunda ± manfiy. 72 dan 2\sqrt{130} ni ayirish.

$$x=\frac{72-2\sqrt{130}}{4}$$

72-2\sqrt{130} ni 4 ga bo'lish.

$$x=-\frac{\sqrt{130}}{2}+18$$

Tenglama yechildi.

$$x=\frac{\sqrt{130}}{2}+18 x=-\frac{\sqrt{130}}{2}+18$$

Kvadratni yakunlash bo'yicha qadamlar

32-2x ga 20-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$640-72x+2x^{2}=57$$

Ikkala tarafdan 640 ni ayirish.

$$-72x+2x^{2}=57-640$$

-583 olish uchun 57 dan 640 ni ayirish.

$$-72x+2x^{2}=-583$$

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

$$2x^{2}-72x=-583$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-72x}{2}=-\frac{583}{2}$$

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

$$x^{2}+\left(-\frac{72}{2}\right)x=-\frac{583}{2}$$

-72 ni 2 ga bo'lish.

$$x^{2}-36x=-\frac{583}{2}$$

-36 ni bo‘lish, x shartining koeffitsienti, 2 ga -18 olish uchun. Keyin, -18 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-36x+\left(-18\right)^{2}=-\frac{583}{2}+\left(-18\right)^{2}$$

-18 kvadratini chiqarish.

$$x^{2}-36x+324=-\frac{583}{2}+324$$

-\frac{583}{2} ni 324 ga qo'shish.

$$x^{2}-36x+324=\frac{65}{2}$$

x^{2}-36x+324 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-18\right)^{2}=\frac{65}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-18\right)^{2}}=\sqrt{\frac{65}{2}}$$

Qisqartirish.

$$x-18=\frac{\sqrt{130}}{2} x-18=-\frac{\sqrt{130}}{2}$$

18 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{130}}{2}+18 x=-\frac{\sqrt{130}}{2}+18$$