4x^2-180x+800=0 eching

$$4 x ^ { 2 } - 180 x + 800 = 0$$

x uchun yechish

$$x=5$$

$$x=40$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$4x^{2}-180x+800=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -180 ni b va 800 ni c bilan almashtiring.

$$x=\frac{-\left(-180\right)±\sqrt{\left(-180\right)^{2}-4\times 4\times 800}}{2\times 4}$$

-180 kvadratini chiqarish.

$$x=\frac{-\left(-180\right)±\sqrt{32400-4\times 4\times 800}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-180\right)±\sqrt{32400-16\times 800}}{2\times 4}$$

-16 ni 800 marotabaga ko'paytirish.

$$x=\frac{-\left(-180\right)±\sqrt{32400-12800}}{2\times 4}$$

32400 ni -12800 ga qo'shish.

$$x=\frac{-\left(-180\right)±\sqrt{19600}}{2\times 4}$$

19600 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-180\right)±140}{2\times 4}$$

-180 ning teskarisi 180 ga teng.

$$x=\frac{180±140}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{180±140}{8}$$

x=\frac{180±140}{8} tenglamasini yeching, bunda ± musbat. 180 ni 140 ga qo'shish.

$$x=\frac{320}{8}$$

320 ni 8 ga bo'lish.

$$x=40$$

x=\frac{180±140}{8} tenglamasini yeching, bunda ± manfiy. 180 dan 140 ni ayirish.

$$x=\frac{40}{8}$$

40 ni 8 ga bo'lish.

$$x=5$$

Tenglama yechildi.

$$x=40 x=5$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$4x^{2}-180x+800=0$$

Tenglamaning ikkala tarafidan 800 ni ayirish.

$$4x^{2}-180x+800-800=-800$$

O‘zidan 800 ayirilsa 0 qoladi.

$$4x^{2}-180x=-800$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-180x}{4}=-\frac{800}{4}$$

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

$$x^{2}+\left(-\frac{180}{4}\right)x=-\frac{800}{4}$$

-180 ni 4 ga bo'lish.

$$x^{2}-45x=-\frac{800}{4}$$

-800 ni 4 ga bo'lish.

$$x^{2}-45x=-200$$

-45 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{45}{2} olish uchun. Keyin, -\frac{45}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-45x+\left(-\frac{45}{2}\right)^{2}=-200+\left(-\frac{45}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{45}{2} kvadratini chiqarish.

$$x^{2}-45x+\frac{2025}{4}=-200+\frac{2025}{4}$$

-200 ni \frac{2025}{4} ga qo'shish.

$$x^{2}-45x+\frac{2025}{4}=\frac{1225}{4}$$

x^{2}-45x+\frac{2025}{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.

$$\left(x-\frac{45}{2}\right)^{2}=\frac{1225}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{45}{2}\right)^{2}}=\sqrt{\frac{1225}{4}}$$

Qisqartirish.

$$x-\frac{45}{2}=\frac{35}{2} x-\frac{45}{2}=-\frac{35}{2}$$

\frac{45}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=40 x=5$$