x^2+1*80x-5*40=0 eching

$$x ^ { 2 } + 1 \cdot 80 x - 5 \cdot 40 = 0$$

x uchun yechish

$$x=30\sqrt{2}-40\approx 2,426406871$$

$$x=-30\sqrt{2}-40\approx -82,426406871$$

Kvadrat tenglamalaridan foydalanish qoidalari

80 hosil qilish uchun 1 va 80 ni ko'paytirish.

$$x^{2}+80x-5\times 40=0$$

200 hosil qilish uchun 5 va 40 ni ko'paytirish.

$$x^{2}+80x-200=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 80 ni b va -200 ni c bilan almashtiring.

$$x=\frac{-80±\sqrt{80^{2}-4\left(-200\right)}}{2}$$

80 kvadratini chiqarish.

$$x=\frac{-80±\sqrt{6400-4\left(-200\right)}}{2}$$

-4 ni -200 marotabaga ko'paytirish.

$$x=\frac{-80±\sqrt{6400+800}}{2}$$

6400 ni 800 ga qo'shish.

$$x=\frac{-80±\sqrt{7200}}{2}$$

7200 ning kvadrat ildizini chiqarish.

$$x=\frac{-80±60\sqrt{2}}{2}$$

x=\frac{-80±60\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. -80 ni 60\sqrt{2} ga qo'shish.

$$x=\frac{60\sqrt{2}-80}{2}$$

-80+60\sqrt{2} ni 2 ga bo'lish.

$$x=30\sqrt{2}-40$$

x=\frac{-80±60\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. -80 dan 60\sqrt{2} ni ayirish.

$$x=\frac{-60\sqrt{2}-80}{2}$$

-80-60\sqrt{2} ni 2 ga bo'lish.

$$x=-30\sqrt{2}-40$$

Tenglama yechildi.

$$x=30\sqrt{2}-40 x=-30\sqrt{2}-40$$

Kvadratni yakunlash bo'yicha qadamlar

80 hosil qilish uchun 1 va 80 ni ko'paytirish.

$$x^{2}+80x-5\times 40=0$$

200 hosil qilish uchun 5 va 40 ni ko'paytirish.

$$x^{2}+80x-200=0$$

200 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}+80x=200$$

80 ni bo‘lish, x shartining koeffitsienti, 2 ga 40 olish uchun. Keyin, 40 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+80x+40^{2}=200+40^{2}$$

40 kvadratini chiqarish.

$$x^{2}+80x+1600=200+1600$$

200 ni 1600 ga qo'shish.

$$x^{2}+80x+1600=1800$$

x^{2}+80x+1600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+40\right)^{2}=1800$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+40\right)^{2}}=\sqrt{1800}$$

Qisqartirish.

$$x+40=30\sqrt{2} x+40=-30\sqrt{2}$$

Tenglamaning ikkala tarafidan 40 ni ayirish.

$$x=30\sqrt{2}-40 x=-30\sqrt{2}-40$$