2q^2+10q+12=q^2 eching

$$2 q ^ { 2 } + 10 q + 12 = q ^ { 2 }$$

q uchun yechish

$$q=\sqrt{13}-5\approx -1,394448725$$

$$q=-\sqrt{13}-5\approx -8,605551275$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan q^{2} ni ayirish.

$$2q^{2}+10q+12-q^{2}=0$$

q^{2} ni olish uchun 2q^{2} va -q^{2} ni birlashtirish.

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

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 12 ni c bilan almashtiring.

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

10 kvadratini chiqarish.

$$q=\frac{-10±\sqrt{100-4\times 12}}{2}$$

-4 ni 12 marotabaga ko'paytirish.

$$q=\frac{-10±\sqrt{100-48}}{2}$$

100 ni -48 ga qo'shish.

$$q=\frac{-10±\sqrt{52}}{2}$$

52 ning kvadrat ildizini chiqarish.

$$q=\frac{-10±2\sqrt{13}}{2}$$

q=\frac{-10±2\sqrt{13}}{2} tenglamasini yeching, bunda ± musbat. -10 ni 2\sqrt{13} ga qo'shish.

$$q=\frac{2\sqrt{13}-10}{2}$$

-10+2\sqrt{13} ni 2 ga bo'lish.

$$q=\sqrt{13}-5$$

q=\frac{-10±2\sqrt{13}}{2} tenglamasini yeching, bunda ± manfiy. -10 dan 2\sqrt{13} ni ayirish.

$$q=\frac{-2\sqrt{13}-10}{2}$$

-10-2\sqrt{13} ni 2 ga bo'lish.

$$q=-\sqrt{13}-5$$

Tenglama yechildi.

$$q=\sqrt{13}-5 q=-\sqrt{13}-5$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan q^{2} ni ayirish.

$$2q^{2}+10q+12-q^{2}=0$$

q^{2} ni olish uchun 2q^{2} va -q^{2} ni birlashtirish.

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

Ikkala tarafdan 12 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

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.

$$q^{2}+10q+5^{2}=-12+5^{2}$$

5 kvadratini chiqarish.

$$q^{2}+10q+25=-12+25$$

-12 ni 25 ga qo'shish.

$$q^{2}+10q+25=13$$

q^{2}+10q+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.

$$\left(q+5\right)^{2}=13$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(q+5\right)^{2}}=\sqrt{13}$$

Qisqartirish.

$$q+5=\sqrt{13} q+5=-\sqrt{13}$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$q=\sqrt{13}-5 q=-\sqrt{13}-5$$