y^2+10=-12y eching

$$y ^ { 2 } + 10 = - 12 y$$

y uchun yechish (complex solution)

$$y=\sqrt{26}-6\approx -0,900980486$$

$$y=-\left(\sqrt{26}+6\right)\approx -11,099019514$$

Kvadrat tenglamalaridan foydalanish qoidalari

12y ni ikki tarafga qo’shing.

$$y^{2}+10+12y=0$$

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.

$$y^{2}+12y+10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 12 ni b va 10 ni c bilan almashtiring.

$$y=\frac{-12±\sqrt{12^{2}-4\times 10}}{2}$$

12 kvadratini chiqarish.

$$y=\frac{-12±\sqrt{144-4\times 10}}{2}$$

-4 ni 10 marotabaga ko'paytirish.

$$y=\frac{-12±\sqrt{144-40}}{2}$$

144 ni -40 ga qo'shish.

$$y=\frac{-12±\sqrt{104}}{2}$$

104 ning kvadrat ildizini chiqarish.

$$y=\frac{-12±2\sqrt{26}}{2}$$

y=\frac{-12±2\sqrt{26}}{2} tenglamasini yeching, bunda ± musbat. -12 ni 2\sqrt{26} ga qo'shish.

$$y=\frac{2\sqrt{26}-12}{2}$$

-12+2\sqrt{26} ni 2 ga bo'lish.

$$y=\sqrt{26}-6$$

y=\frac{-12±2\sqrt{26}}{2} tenglamasini yeching, bunda ± manfiy. -12 dan 2\sqrt{26} ni ayirish.

$$y=\frac{-2\sqrt{26}-12}{2}$$

-12-2\sqrt{26} ni 2 ga bo'lish.

$$y=-\sqrt{26}-6$$

Tenglama yechildi.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$

Kvadratni yakunlash bo'yicha qadamlar

12y ni ikki tarafga qo’shing.

$$y^{2}+10+12y=0$$

Ikkala tarafdan 10 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$y^{2}+12y=-10$$

12 ni bo‘lish, x shartining koeffitsienti, 2 ga 6 olish uchun. Keyin, 6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}+12y+6^{2}=-10+6^{2}$$

6 kvadratini chiqarish.

$$y^{2}+12y+36=-10+36$$

-10 ni 36 ga qo'shish.

$$y^{2}+12y+36=26$$

y^{2}+12y+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y+6\right)^{2}=26$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y+6\right)^{2}}=\sqrt{26}$$

Qisqartirish.

$$y+6=\sqrt{26} y+6=-\sqrt{26}$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$

y uchun yechish

$$y=\sqrt{26}-6\approx -0,900980486$$

$$y=-\sqrt{26}-6\approx -11,099019514$$

Kvadrat tenglamalaridan foydalanish qoidalari

12y ni ikki tarafga qo’shing.

$$y^{2}+10+12y=0$$

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.

$$y^{2}+12y+10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 12 ni b va 10 ni c bilan almashtiring.

$$y=\frac{-12±\sqrt{12^{2}-4\times 10}}{2}$$

12 kvadratini chiqarish.

$$y=\frac{-12±\sqrt{144-4\times 10}}{2}$$

-4 ni 10 marotabaga ko'paytirish.

$$y=\frac{-12±\sqrt{144-40}}{2}$$

144 ni -40 ga qo'shish.

$$y=\frac{-12±\sqrt{104}}{2}$$

104 ning kvadrat ildizini chiqarish.

$$y=\frac{-12±2\sqrt{26}}{2}$$

y=\frac{-12±2\sqrt{26}}{2} tenglamasini yeching, bunda ± musbat. -12 ni 2\sqrt{26} ga qo'shish.

$$y=\frac{2\sqrt{26}-12}{2}$$

-12+2\sqrt{26} ni 2 ga bo'lish.

$$y=\sqrt{26}-6$$

y=\frac{-12±2\sqrt{26}}{2} tenglamasini yeching, bunda ± manfiy. -12 dan 2\sqrt{26} ni ayirish.

$$y=\frac{-2\sqrt{26}-12}{2}$$

-12-2\sqrt{26} ni 2 ga bo'lish.

$$y=-\sqrt{26}-6$$

Tenglama yechildi.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$

Kvadratni yakunlash bo'yicha qadamlar

12y ni ikki tarafga qo’shing.

$$y^{2}+10+12y=0$$

Ikkala tarafdan 10 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$y^{2}+12y=-10$$

12 ni bo‘lish, x shartining koeffitsienti, 2 ga 6 olish uchun. Keyin, 6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}+12y+6^{2}=-10+6^{2}$$

6 kvadratini chiqarish.

$$y^{2}+12y+36=-10+36$$

-10 ni 36 ga qo'shish.

$$y^{2}+12y+36=26$$

y^{2}+12y+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y+6\right)^{2}=26$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y+6\right)^{2}}=\sqrt{26}$$

Qisqartirish.

$$y+6=\sqrt{26} y+6=-\sqrt{26}$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$y=\sqrt{26}-6 y=-\sqrt{26}-6$$