4m^2-5m-4=0 eching

$$4 m ^ { 2 } - 5 m - 4 = 0$$

m uchun yechish

$$m = \frac{\sqrt{89} + 5}{8} \approx 1,804247642$$

$$m=\frac{5-\sqrt{89}}{8}\approx -0,554247642$$

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.

$$4m^{2}-5m-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -5 ni b va -4 ni c bilan almashtiring.

$$m=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 4\left(-4\right)}}{2\times 4}$$

-5 kvadratini chiqarish.

$$m=\frac{-\left(-5\right)±\sqrt{25-4\times 4\left(-4\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$m=\frac{-\left(-5\right)±\sqrt{25-16\left(-4\right)}}{2\times 4}$$

-16 ni -4 marotabaga ko'paytirish.

$$m=\frac{-\left(-5\right)±\sqrt{25+64}}{2\times 4}$$

25 ni 64 ga qo'shish.

$$m=\frac{-\left(-5\right)±\sqrt{89}}{2\times 4}$$

-5 ning teskarisi 5 ga teng.

$$m=\frac{5±\sqrt{89}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$m=\frac{5±\sqrt{89}}{8}$$

m=\frac{5±\sqrt{89}}{8} tenglamasini yeching, bunda ± musbat. 5 ni \sqrt{89} ga qo'shish.

$$m=\frac{\sqrt{89}+5}{8}$$

m=\frac{5±\sqrt{89}}{8} tenglamasini yeching, bunda ± manfiy. 5 dan \sqrt{89} ni ayirish.

$$m=\frac{5-\sqrt{89}}{8}$$

Tenglama yechildi.

$$m=\frac{\sqrt{89}+5}{8} m=\frac{5-\sqrt{89}}{8}$$

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.

$$4m^{2}-5m-4=0$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$4m^{2}-5m-4-\left(-4\right)=-\left(-4\right)$$

O‘zidan -4 ayirilsa 0 qoladi.

$$4m^{2}-5m=-\left(-4\right)$$

0 dan -4 ni ayirish.

$$4m^{2}-5m=4$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4m^{2}-5m}{4}=\frac{4}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$m^{2}-\frac{5}{4}m=\frac{4}{4}$$

4 ni 4 ga bo'lish.

$$m^{2}-\frac{5}{4}m=1$$

-\frac{5}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{8} olish uchun. Keyin, -\frac{5}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}-\frac{5}{4}m+\left(-\frac{5}{8}\right)^{2}=1+\left(-\frac{5}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{8} kvadratini chiqarish.

$$m^{2}-\frac{5}{4}m+\frac{25}{64}=1+\frac{25}{64}$$

1 ni \frac{25}{64} ga qo'shish.

$$m^{2}-\frac{5}{4}m+\frac{25}{64}=\frac{89}{64}$$

m^{2}-\frac{5}{4}m+\frac{25}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m-\frac{5}{8}\right)^{2}=\frac{89}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-\frac{5}{8}\right)^{2}}=\sqrt{\frac{89}{64}}$$

Qisqartirish.

$$m-\frac{5}{8}=\frac{\sqrt{89}}{8} m-\frac{5}{8}=-\frac{\sqrt{89}}{8}$$

\frac{5}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$m=\frac{\sqrt{89}+5}{8} m=\frac{5-\sqrt{89}}{8}$$