g^2+7g=0 eching

$$g ^ { 2 } + 7 g = 0$$

g uchun yechish

$$g=-7$$

$$g=0$$

Faktorlash qadamlari

g omili.

$$g\left(g+7\right)=0$$

Tenglamani yechish uchun g=0 va g+7=0 ni yeching.

$$g=0 g=-7$$

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.

$$g^{2}+7g=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 7 ni b va 0 ni c bilan almashtiring.

$$g=\frac{-7±\sqrt{7^{2}}}{2}$$

7^{2} ning kvadrat ildizini chiqarish.

$$g=\frac{-7±7}{2}$$

g=\frac{-7±7}{2} tenglamasini yeching, bunda ± musbat. -7 ni 7 ga qo'shish.

$$g=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$g=0$$

g=\frac{-7±7}{2} tenglamasini yeching, bunda ± manfiy. -7 dan 7 ni ayirish.

$$g=-\frac{14}{2}$$

-14 ni 2 ga bo'lish.

$$g=-7$$

Tenglama yechildi.

$$g=0 g=-7$$

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.

$$g^{2}+7g=0$$

7 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{2} olish uchun. Keyin, \frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$g^{2}+7g+\left(\frac{7}{2}\right)^{2}=\left(\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{2} kvadratini chiqarish.

$$g^{2}+7g+\frac{49}{4}=\frac{49}{4}$$

g^{2}+7g+\frac{49}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(g+\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(g+\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$g+\frac{7}{2}=\frac{7}{2} g+\frac{7}{2}=-\frac{7}{2}$$

Tenglamaning ikkala tarafidan \frac{7}{2} ni ayirish.

$$g=0 g=-7$$