q^2-36q+540=3q^2-72q+540 eching

$$q ^ { 2 } - 36 q + 540 = 3 q ^ { 2 } - 72 q + 540$$

q uchun yechish

$$q=18$$

$$q=0$$

Faktorlash qadamlari

Ikkala tarafdan 3q^{2} ni ayirish.

$$q^{2}-36q+540-3q^{2}=-72q+540$$

-2q^{2} ni olish uchun q^{2} va -3q^{2} ni birlashtirish.

$$-2q^{2}-36q+540=-72q+540$$

72q ni ikki tarafga qo’shing.

$$-2q^{2}-36q+540+72q=540$$

36q ni olish uchun -36q va 72q ni birlashtirish.

$$-2q^{2}+36q+540=540$$

Ikkala tarafdan 540 ni ayirish.

$$-2q^{2}+36q+540-540=0$$

0 olish uchun 540 dan 540 ni ayirish.

$$-2q^{2}+36q=0$$

q omili.

$$q\left(-2q+36\right)=0$$

Tenglamani yechish uchun q=0 va -2q+36=0 ni yeching.

$$q=0 q=18$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 3q^{2} ni ayirish.

$$q^{2}-36q+540-3q^{2}=-72q+540$$

-2q^{2} ni olish uchun q^{2} va -3q^{2} ni birlashtirish.

$$-2q^{2}-36q+540=-72q+540$$

72q ni ikki tarafga qo’shing.

$$-2q^{2}-36q+540+72q=540$$

36q ni olish uchun -36q va 72q ni birlashtirish.

$$-2q^{2}+36q+540=540$$

Ikkala tarafdan 540 ni ayirish.

$$-2q^{2}+36q+540-540=0$$

0 olish uchun 540 dan 540 ni ayirish.

$$-2q^{2}+36q=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 36 ni b va 0 ni c bilan almashtiring.

$$q=\frac{-36±\sqrt{36^{2}}}{2\left(-2\right)}$$

36^{2} ning kvadrat ildizini chiqarish.

$$q=\frac{-36±36}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$q=\frac{-36±36}{-4}$$

q=\frac{-36±36}{-4} tenglamasini yeching, bunda ± musbat. -36 ni 36 ga qo'shish.

$$q=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$q=0$$

q=\frac{-36±36}{-4} tenglamasini yeching, bunda ± manfiy. -36 dan 36 ni ayirish.

$$q=-\frac{72}{-4}$$

-72 ni -4 ga bo'lish.

$$q=18$$

Tenglama yechildi.

$$q=0 q=18$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 3q^{2} ni ayirish.

$$q^{2}-36q+540-3q^{2}=-72q+540$$

-2q^{2} ni olish uchun q^{2} va -3q^{2} ni birlashtirish.

$$-2q^{2}-36q+540=-72q+540$$

72q ni ikki tarafga qo’shing.

$$-2q^{2}-36q+540+72q=540$$

36q ni olish uchun -36q va 72q ni birlashtirish.

$$-2q^{2}+36q+540=540$$

Ikkala tarafdan 540 ni ayirish.

$$-2q^{2}+36q=540-540$$

0 olish uchun 540 dan 540 ni ayirish.

$$-2q^{2}+36q=0$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2q^{2}+36q}{-2}=\frac{0}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$q^{2}+\frac{36}{-2}q=\frac{0}{-2}$$

36 ni -2 ga bo'lish.

$$q^{2}-18q=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$q^{2}-18q=0$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$q^{2}-18q+\left(-9\right)^{2}=\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$q^{2}-18q+81=81$$

q^{2}-18q+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(q-9\right)^{2}=81$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(q-9\right)^{2}}=\sqrt{81}$$

Qisqartirish.

$$q-9=9 q-9=-9$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$q=18 q=0$$