8+3g^2-9g=188 eching

$$8 + 3 g ^ { 2 } - 9 g = 188$$

g uchun yechish

$$g = \frac{\sqrt{249} + 3}{2} \approx 9,389866919$$

$$g=\frac{3-\sqrt{249}}{2}\approx -6,389866919$$

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.

$$3g^{2}-9g+8=188$$

Tenglamaning ikkala tarafidan 188 ni ayirish.

$$3g^{2}-9g+8-188=188-188$$

O‘zidan 188 ayirilsa 0 qoladi.

$$3g^{2}-9g+8-188=0$$

8 dan 188 ni ayirish.

$$3g^{2}-9g-180=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -9 ni b va -180 ni c bilan almashtiring.

$$g=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 3\left(-180\right)}}{2\times 3}$$

-9 kvadratini chiqarish.

$$g=\frac{-\left(-9\right)±\sqrt{81-4\times 3\left(-180\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$g=\frac{-\left(-9\right)±\sqrt{81-12\left(-180\right)}}{2\times 3}$$

-12 ni -180 marotabaga ko'paytirish.

$$g=\frac{-\left(-9\right)±\sqrt{81+2160}}{2\times 3}$$

81 ni 2160 ga qo'shish.

$$g=\frac{-\left(-9\right)±\sqrt{2241}}{2\times 3}$$

2241 ning kvadrat ildizini chiqarish.

$$g=\frac{-\left(-9\right)±3\sqrt{249}}{2\times 3}$$

-9 ning teskarisi 9 ga teng.

$$g=\frac{9±3\sqrt{249}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$g=\frac{9±3\sqrt{249}}{6}$$

g=\frac{9±3\sqrt{249}}{6} tenglamasini yeching, bunda ± musbat. 9 ni 3\sqrt{249} ga qo'shish.

$$g=\frac{3\sqrt{249}+9}{6}$$

9+3\sqrt{249} ni 6 ga bo'lish.

$$g=\frac{\sqrt{249}+3}{2}$$

g=\frac{9±3\sqrt{249}}{6} tenglamasini yeching, bunda ± manfiy. 9 dan 3\sqrt{249} ni ayirish.

$$g=\frac{9-3\sqrt{249}}{6}$$

9-3\sqrt{249} ni 6 ga bo'lish.

$$g=\frac{3-\sqrt{249}}{2}$$

Tenglama yechildi.

$$g=\frac{\sqrt{249}+3}{2} g=\frac{3-\sqrt{249}}{2}$$

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.

$$3g^{2}-9g+8=188$$

Tenglamaning ikkala tarafidan 8 ni ayirish.

$$3g^{2}-9g+8-8=188-8$$

O‘zidan 8 ayirilsa 0 qoladi.

$$3g^{2}-9g=188-8$$

188 dan 8 ni ayirish.

$$3g^{2}-9g=180$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3g^{2}-9g}{3}=\frac{180}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$g^{2}+\left(-\frac{9}{3}\right)g=\frac{180}{3}$$

-9 ni 3 ga bo'lish.

$$g^{2}-3g=\frac{180}{3}$$

180 ni 3 ga bo'lish.

$$g^{2}-3g=60$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$g^{2}-3g+\left(-\frac{3}{2}\right)^{2}=60+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$g^{2}-3g+\frac{9}{4}=60+\frac{9}{4}$$

60 ni \frac{9}{4} ga qo'shish.

$$g^{2}-3g+\frac{9}{4}=\frac{249}{4}$$

g^{2}-3g+\frac{9}{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.

$$\left(g-\frac{3}{2}\right)^{2}=\frac{249}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(g-\frac{3}{2}\right)^{2}}=\sqrt{\frac{249}{4}}$$

Qisqartirish.

$$g-\frac{3}{2}=\frac{\sqrt{249}}{2} g-\frac{3}{2}=-\frac{\sqrt{249}}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$g=\frac{\sqrt{249}+3}{2} g=\frac{3-\sqrt{249}}{2}$$