x^2+16x+4=-10 eching

$${ x }^{ 2 } +16x+4=-10$$

x uchun yechish

$$x=5\sqrt{2}-8\approx -0,928932188$$

$$x=-5\sqrt{2}-8\approx -15,071067812$$

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.

$$x^{2}+16x+4=-10$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+16x+4-\left(-10\right)=-10-\left(-10\right)$$

O‘zidan -10 ayirilsa 0 qoladi.

$$x^{2}+16x+4-\left(-10\right)=0$$

4 dan -10 ni ayirish.

$$x^{2}+16x+14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 16 ni b va 14 ni c bilan almashtiring.

$$x=\frac{-16±\sqrt{16^{2}-4\times 14}}{2}$$

16 kvadratini chiqarish.

$$x=\frac{-16±\sqrt{256-4\times 14}}{2}$$

-4 ni 14 marotabaga ko'paytirish.

$$x=\frac{-16±\sqrt{256-56}}{2}$$

256 ni -56 ga qo'shish.

$$x=\frac{-16±\sqrt{200}}{2}$$

200 ning kvadrat ildizini chiqarish.

$$x=\frac{-16±10\sqrt{2}}{2}$$

x=\frac{-16±10\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. -16 ni 10\sqrt{2} ga qo'shish.

$$x=\frac{10\sqrt{2}-16}{2}$$

-16+10\sqrt{2} ni 2 ga bo'lish.

$$x=5\sqrt{2}-8$$

x=\frac{-16±10\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. -16 dan 10\sqrt{2} ni ayirish.

$$x=\frac{-10\sqrt{2}-16}{2}$$

-16-10\sqrt{2} ni 2 ga bo'lish.

$$x=-5\sqrt{2}-8$$

Tenglama yechildi.

$$x=5\sqrt{2}-8 x=-5\sqrt{2}-8$$

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.

$$x^{2}+16x+4=-10$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x^{2}+16x+4-4=-10-4$$

O‘zidan 4 ayirilsa 0 qoladi.

$$x^{2}+16x=-10-4$$

-10 dan 4 ni ayirish.

$$x^{2}+16x=-14$$

16 ni bo‘lish, x shartining koeffitsienti, 2 ga 8 olish uchun. Keyin, 8 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+16x+8^{2}=-14+8^{2}$$

8 kvadratini chiqarish.

$$x^{2}+16x+64=-14+64$$

-14 ni 64 ga qo'shish.

$$x^{2}+16x+64=50$$

x^{2}+16x+64 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+8\right)^{2}=50$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{50}$$

Qisqartirish.

$$x+8=5\sqrt{2} x+8=-5\sqrt{2}$$

Tenglamaning ikkala tarafidan 8 ni ayirish.

$$x=5\sqrt{2}-8 x=-5\sqrt{2}-8$$