y^2+10y^-400=0 eching

$${ y }^{ 2 } +10 { y }^{ } -400=0$$

y uchun yechish

$$y=5\sqrt{17}-5\approx 15,615528128$$

$$y=-5\sqrt{17}-5\approx -25,615528128$$

Kvadrat tenglamalaridan foydalanish qoidalari

1 daraja ko‘rsatkichini y ga hisoblang va y ni qiymatni oling.

$$y^{2}+10y-400=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 10 ni b va -400 ni c bilan almashtiring.

$$y=\frac{-10±\sqrt{10^{2}-4\left(-400\right)}}{2}$$

10 kvadratini chiqarish.

$$y=\frac{-10±\sqrt{100-4\left(-400\right)}}{2}$$

-4 ni -400 marotabaga ko'paytirish.

$$y=\frac{-10±\sqrt{100+1600}}{2}$$

100 ni 1600 ga qo'shish.

$$y=\frac{-10±\sqrt{1700}}{2}$$

1700 ning kvadrat ildizini chiqarish.

$$y=\frac{-10±10\sqrt{17}}{2}$$

y=\frac{-10±10\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. -10 ni 10\sqrt{17} ga qo'shish.

$$y=\frac{10\sqrt{17}-10}{2}$$

-10+10\sqrt{17} ni 2 ga bo'lish.

$$y=5\sqrt{17}-5$$

y=\frac{-10±10\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. -10 dan 10\sqrt{17} ni ayirish.

$$y=\frac{-10\sqrt{17}-10}{2}$$

-10-10\sqrt{17} ni 2 ga bo'lish.

$$y=-5\sqrt{17}-5$$

Tenglama yechildi.

$$y=5\sqrt{17}-5 y=-5\sqrt{17}-5$$

Kvadratni yakunlash bo'yicha qadamlar

1 daraja ko‘rsatkichini y ga hisoblang va y ni qiymatni oling.

$$y^{2}+10y-400=0$$

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

$$y^{2}+10y=400$$

10 ni bo‘lish, x shartining koeffitsienti, 2 ga 5 olish uchun. Keyin, 5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}+10y+5^{2}=400+5^{2}$$

5 kvadratini chiqarish.

$$y^{2}+10y+25=400+25$$

400 ni 25 ga qo'shish.

$$y^{2}+10y+25=425$$

y^{2}+10y+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y+5\right)^{2}=425$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y+5\right)^{2}}=\sqrt{425}$$

Qisqartirish.

$$y+5=5\sqrt{17} y+5=-5\sqrt{17}$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$y=5\sqrt{17}-5 y=-5\sqrt{17}-5$$