x^2+40x-75=0 eching

$$x ^ { 2 } + 40 x - 75 = 0$$

x uchun yechish

$$x=5\sqrt{19}-20\approx 1,794494718$$

$$x=-5\sqrt{19}-20\approx -41,794494718$$

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.

$$x^{2}+40x-75=0$$

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 -75 ni c bilan almashtiring.

$$x=\frac{-40±\sqrt{40^{2}-4\left(-75\right)}}{2}$$

40 kvadratini chiqarish.

$$x=\frac{-40±\sqrt{1600-4\left(-75\right)}}{2}$$

-4 ni -75 marotabaga ko'paytirish.

$$x=\frac{-40±\sqrt{1600+300}}{2}$$

1600 ni 300 ga qo'shish.

$$x=\frac{-40±\sqrt{1900}}{2}$$

1900 ning kvadrat ildizini chiqarish.

$$x=\frac{-40±10\sqrt{19}}{2}$$

x=\frac{-40±10\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. -40 ni 10\sqrt{19} ga qo'shish.

$$x=\frac{10\sqrt{19}-40}{2}$$

-40+10\sqrt{19} ni 2 ga bo'lish.

$$x=5\sqrt{19}-20$$

x=\frac{-40±10\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. -40 dan 10\sqrt{19} ni ayirish.

$$x=\frac{-10\sqrt{19}-40}{2}$$

-40-10\sqrt{19} ni 2 ga bo'lish.

$$x=-5\sqrt{19}-20$$

Tenglama yechildi.

$$x=5\sqrt{19}-20 x=-5\sqrt{19}-20$$

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.

$$x^{2}+40x-75=0$$

75 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+40x-75-\left(-75\right)=-\left(-75\right)$$

O‘zidan -75 ayirilsa 0 qoladi.

$$x^{2}+40x=-\left(-75\right)$$

0 dan -75 ni ayirish.

$$x^{2}+40x=75$$

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.

$$x^{2}+40x+20^{2}=75+20^{2}$$

20 kvadratini chiqarish.

$$x^{2}+40x+400=75+400$$

75 ni 400 ga qo'shish.

$$x^{2}+40x+400=475$$

x^{2}+40x+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.

$$\left(x+20\right)^{2}=475$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+20\right)^{2}}=\sqrt{475}$$

Qisqartirish.

$$x+20=5\sqrt{19} x+20=-5\sqrt{19}$$

Tenglamaning ikkala tarafidan 20 ni ayirish.

$$x=5\sqrt{19}-20 x=-5\sqrt{19}-20$$