x^2-1200x+40000=0 eching

$${ x }^{ 2 } -1200x+40000 = 0$$

x uchun yechish

$$x=400\sqrt{2}+600\approx 1165,685424949$$

$$x=600-400\sqrt{2}\approx 34,314575051$$

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.

$$x^{2}-1200x+40000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1200 ni b va 40000 ni c bilan almashtiring.

$$x=\frac{-\left(-1200\right)±\sqrt{\left(-1200\right)^{2}-4\times 40000}}{2}$$

-1200 kvadratini chiqarish.

$$x=\frac{-\left(-1200\right)±\sqrt{1440000-4\times 40000}}{2}$$

-4 ni 40000 marotabaga ko'paytirish.

$$x=\frac{-\left(-1200\right)±\sqrt{1440000-160000}}{2}$$

1440000 ni -160000 ga qo'shish.

$$x=\frac{-\left(-1200\right)±\sqrt{1280000}}{2}$$

1280000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1200\right)±800\sqrt{2}}{2}$$

-1200 ning teskarisi 1200 ga teng.

$$x=\frac{1200±800\sqrt{2}}{2}$$

x=\frac{1200±800\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 1200 ni 800\sqrt{2} ga qo'shish.

$$x=\frac{800\sqrt{2}+1200}{2}$$

1200+800\sqrt{2} ni 2 ga bo'lish.

$$x=400\sqrt{2}+600$$

x=\frac{1200±800\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 1200 dan 800\sqrt{2} ni ayirish.

$$x=\frac{1200-800\sqrt{2}}{2}$$

1200-800\sqrt{2} ni 2 ga bo'lish.

$$x=600-400\sqrt{2}$$

Tenglama yechildi.

$$x=400\sqrt{2}+600 x=600-400\sqrt{2}$$

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.

$$x^{2}-1200x+40000=0$$

Tenglamaning ikkala tarafidan 40000 ni ayirish.

$$x^{2}-1200x+40000-40000=-40000$$

O‘zidan 40000 ayirilsa 0 qoladi.

$$x^{2}-1200x=-40000$$

-1200 ni bo‘lish, x shartining koeffitsienti, 2 ga -600 olish uchun. Keyin, -600 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-1200x+\left(-600\right)^{2}=-40000+\left(-600\right)^{2}$$

-600 kvadratini chiqarish.

$$x^{2}-1200x+360000=-40000+360000$$

-40000 ni 360000 ga qo'shish.

$$x^{2}-1200x+360000=320000$$

x^{2}-1200x+360000 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-600\right)^{2}=320000$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-600\right)^{2}}=\sqrt{320000}$$

Qisqartirish.

$$x-600=400\sqrt{2} x-600=-400\sqrt{2}$$

600 ni tenglamaning ikkala tarafiga qo'shish.

$$x=400\sqrt{2}+600 x=600-400\sqrt{2}$$