m^2-6m-25=0 eching

$$m ^ { 2 } - 6 m - 25 = 0$$

m uchun yechish

$$m=\sqrt{34}+3\approx 8,830951895$$

$$m=3-\sqrt{34}\approx -2,830951895$$

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.

$$m^{2}-6m-25=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va -25 ni c bilan almashtiring.

$$m=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-25\right)}}{2}$$

-6 kvadratini chiqarish.

$$m=\frac{-\left(-6\right)±\sqrt{36-4\left(-25\right)}}{2}$$

-4 ni -25 marotabaga ko'paytirish.

$$m=\frac{-\left(-6\right)±\sqrt{36+100}}{2}$$

36 ni 100 ga qo'shish.

$$m=\frac{-\left(-6\right)±\sqrt{136}}{2}$$

136 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-6\right)±2\sqrt{34}}{2}$$

-6 ning teskarisi 6 ga teng.

$$m=\frac{6±2\sqrt{34}}{2}$$

m=\frac{6±2\sqrt{34}}{2} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{34} ga qo'shish.

$$m=\frac{2\sqrt{34}+6}{2}$$

6+2\sqrt{34} ni 2 ga bo'lish.

$$m=\sqrt{34}+3$$

m=\frac{6±2\sqrt{34}}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{34} ni ayirish.

$$m=\frac{6-2\sqrt{34}}{2}$$

6-2\sqrt{34} ni 2 ga bo'lish.

$$m=3-\sqrt{34}$$

Tenglama yechildi.

$$m=\sqrt{34}+3 m=3-\sqrt{34}$$

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.

$$m^{2}-6m-25=0$$

25 ni tenglamaning ikkala tarafiga qo'shish.

$$m^{2}-6m-25-\left(-25\right)=-\left(-25\right)$$

O‘zidan -25 ayirilsa 0 qoladi.

$$m^{2}-6m=-\left(-25\right)$$

0 dan -25 ni ayirish.

$$m^{2}-6m=25$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}-6m+\left(-3\right)^{2}=25+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$m^{2}-6m+9=25+9$$

25 ni 9 ga qo'shish.

$$m^{2}-6m+9=34$$

m^{2}-6m+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m-3\right)^{2}=34$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-3\right)^{2}}=\sqrt{34}$$

Qisqartirish.

$$m-3=\sqrt{34} m-3=-\sqrt{34}$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$m=\sqrt{34}+3 m=3-\sqrt{34}$$