m^2+6m+13+m^2+16=45 eching

$$m ^ { 2 } + 6 m + 13 + m ^ { 2 } + 16 = 45$$

m uchun yechish

$$m = \frac{\sqrt{41} - 3}{2} \approx 1,701562119$$

$$m=\frac{-\sqrt{41}-3}{2}\approx -4,701562119$$

Kvadrat tenglamalaridan foydalanish qoidalari

2m^{2} ni olish uchun m^{2} va m^{2} ni birlashtirish.

$$2m^{2}+6m+13+16=45$$

29 olish uchun 13 va 16'ni qo'shing.

$$2m^{2}+6m+29=45$$

Ikkala tarafdan 45 ni ayirish.

$$2m^{2}+6m+29-45=0$$

-16 olish uchun 29 dan 45 ni ayirish.

$$2m^{2}+6m-16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 6 ni b va -16 ni c bilan almashtiring.

$$m=\frac{-6±\sqrt{6^{2}-4\times 2\left(-16\right)}}{2\times 2}$$

6 kvadratini chiqarish.

$$m=\frac{-6±\sqrt{36-4\times 2\left(-16\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$m=\frac{-6±\sqrt{36-8\left(-16\right)}}{2\times 2}$$

-8 ni -16 marotabaga ko'paytirish.

$$m=\frac{-6±\sqrt{36+128}}{2\times 2}$$

36 ni 128 ga qo'shish.

$$m=\frac{-6±\sqrt{164}}{2\times 2}$$

164 ning kvadrat ildizini chiqarish.

$$m=\frac{-6±2\sqrt{41}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$m=\frac{-6±2\sqrt{41}}{4}$$

m=\frac{-6±2\sqrt{41}}{4} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{41} ga qo'shish.

$$m=\frac{2\sqrt{41}-6}{4}$$

-6+2\sqrt{41} ni 4 ga bo'lish.

$$m=\frac{\sqrt{41}-3}{2}$$

m=\frac{-6±2\sqrt{41}}{4} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{41} ni ayirish.

$$m=\frac{-2\sqrt{41}-6}{4}$$

-6-2\sqrt{41} ni 4 ga bo'lish.

$$m=\frac{-\sqrt{41}-3}{2}$$

Tenglama yechildi.

$$m=\frac{\sqrt{41}-3}{2} m=\frac{-\sqrt{41}-3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2m^{2} ni olish uchun m^{2} va m^{2} ni birlashtirish.

$$2m^{2}+6m+13+16=45$$

29 olish uchun 13 va 16'ni qo'shing.

$$2m^{2}+6m+29=45$$

Ikkala tarafdan 29 ni ayirish.

$$2m^{2}+6m=45-29$$

16 olish uchun 45 dan 29 ni ayirish.

$$2m^{2}+6m=16$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2m^{2}+6m}{2}=\frac{16}{2}$$

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

$$m^{2}+\frac{6}{2}m=\frac{16}{2}$$

6 ni 2 ga bo'lish.

$$m^{2}+3m=\frac{16}{2}$$

16 ni 2 ga bo'lish.

$$m^{2}+3m=8$$

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.

$$m^{2}+3m+\left(\frac{3}{2}\right)^{2}=8+\left(\frac{3}{2}\right)^{2}$$

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

$$m^{2}+3m+\frac{9}{4}=8+\frac{9}{4}$$

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

$$m^{2}+3m+\frac{9}{4}=\frac{41}{4}$$

m^{2}+3m+\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.

$$\left(m+\frac{3}{2}\right)^{2}=\frac{41}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m+\frac{3}{2}\right)^{2}}=\sqrt{\frac{41}{4}}$$

Qisqartirish.

$$m+\frac{3}{2}=\frac{\sqrt{41}}{2} m+\frac{3}{2}=-\frac{\sqrt{41}}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$m=\frac{\sqrt{41}-3}{2} m=\frac{-\sqrt{41}-3}{2}$$