m^2-40m-56=0 eching

$${ m }^{ 2 } -40m-56 = 0$$

m uchun yechish

$$m=2\sqrt{114}+20\approx 41,354156504$$

$$m=20-2\sqrt{114}\approx -1,354156504$$

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.

$$m^{2}-40m-56=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -40 ni b va -56 ni c bilan almashtiring.

$$m=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\left(-56\right)}}{2}$$

-40 kvadratini chiqarish.

$$m=\frac{-\left(-40\right)±\sqrt{1600-4\left(-56\right)}}{2}$$

-4 ni -56 marotabaga ko'paytirish.

$$m=\frac{-\left(-40\right)±\sqrt{1600+224}}{2}$$

1600 ni 224 ga qo'shish.

$$m=\frac{-\left(-40\right)±\sqrt{1824}}{2}$$

1824 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-40\right)±4\sqrt{114}}{2}$$

-40 ning teskarisi 40 ga teng.

$$m=\frac{40±4\sqrt{114}}{2}$$

m=\frac{40±4\sqrt{114}}{2} tenglamasini yeching, bunda ± musbat. 40 ni 4\sqrt{114} ga qo'shish.

$$m=\frac{4\sqrt{114}+40}{2}$$

40+4\sqrt{114} ni 2 ga bo'lish.

$$m=2\sqrt{114}+20$$

m=\frac{40±4\sqrt{114}}{2} tenglamasini yeching, bunda ± manfiy. 40 dan 4\sqrt{114} ni ayirish.

$$m=\frac{40-4\sqrt{114}}{2}$$

40-4\sqrt{114} ni 2 ga bo'lish.

$$m=20-2\sqrt{114}$$

Tenglama yechildi.

$$m=2\sqrt{114}+20 m=20-2\sqrt{114}$$

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.

$$m^{2}-40m-56=0$$

56 ni tenglamaning ikkala tarafiga qo'shish.

$$m^{2}-40m-56-\left(-56\right)=-\left(-56\right)$$

O‘zidan -56 ayirilsa 0 qoladi.

$$m^{2}-40m=-\left(-56\right)$$

0 dan -56 ni ayirish.

$$m^{2}-40m=56$$

-40 ni bo‘lish, x shartining koeffitsienti, 2 ga -20 olish uchun. Keyin, -20 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}-40m+\left(-20\right)^{2}=56+\left(-20\right)^{2}$$

-20 kvadratini chiqarish.

$$m^{2}-40m+400=56+400$$

56 ni 400 ga qo'shish.

$$m^{2}-40m+400=456$$

m^{2}-40m+400 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m-20\right)^{2}=456$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-20\right)^{2}}=\sqrt{456}$$

Qisqartirish.

$$m-20=2\sqrt{114} m-20=-2\sqrt{114}$$

20 ni tenglamaning ikkala tarafiga qo'shish.

$$m=2\sqrt{114}+20 m=20-2\sqrt{114}$$