x^2+2x-5=05*2x^2 eching

$${ x }^{ 2 } +2x-5=05 \times 2 { x }^{ 2 }$$

x uchun yechish (complex solution)

$$x=\sqrt{6}-1\approx 1,449489743$$

$$x=-\left(\sqrt{6}+1\right)\approx -3,449489743$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$x^{2}+2x-5=0\times 2x^{2}$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$x^{2}+2x-5=0x^{2}$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}+2x-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va -5 ni c bilan almashtiring.

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

2 kvadratini chiqarish.

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

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+20}}{2}$$

4 ni 20 ga qo'shish.

$$x=\frac{-2±\sqrt{24}}{2}$$

24 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{6}}{2}$$

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

$$x=\frac{2\sqrt{6}-2}{2}$$

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

$$x=\sqrt{6}-1$$

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

$$x=\frac{-2\sqrt{6}-2}{2}$$

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

$$x=-\sqrt{6}-1$$

Tenglama yechildi.

$$x=\sqrt{6}-1 x=-\sqrt{6}-1$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$x^{2}+2x-5=0\times 2x^{2}$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$x^{2}+2x-5=0x^{2}$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}+2x-5=0$$

5 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}+2x=5$$

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=5+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=5+1$$

5 ni 1 ga qo'shish.

$$x^{2}+2x+1=6$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=6$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{6}$$

Qisqartirish.

$$x+1=\sqrt{6} x+1=-\sqrt{6}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\sqrt{6}-1 x=-\sqrt{6}-1$$

x uchun yechish

$$x=\sqrt{6}-1\approx 1,449489743$$

$$x=-\sqrt{6}-1\approx -3,449489743$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$x^{2}+2x-5=0\times 2x^{2}$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$x^{2}+2x-5=0x^{2}$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}+2x-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va -5 ni c bilan almashtiring.

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

2 kvadratini chiqarish.

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

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+20}}{2}$$

4 ni 20 ga qo'shish.

$$x=\frac{-2±\sqrt{24}}{2}$$

24 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{6}}{2}$$

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

$$x=\frac{2\sqrt{6}-2}{2}$$

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

$$x=\sqrt{6}-1$$

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

$$x=\frac{-2\sqrt{6}-2}{2}$$

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

$$x=-\sqrt{6}-1$$

Tenglama yechildi.

$$x=\sqrt{6}-1 x=-\sqrt{6}-1$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$x^{2}+2x-5=0\times 2x^{2}$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$x^{2}+2x-5=0x^{2}$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$x^{2}+2x-5=0$$

5 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}+2x=5$$

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=5+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=5+1$$

5 ni 1 ga qo'shish.

$$x^{2}+2x+1=6$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=6$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{6}$$

Qisqartirish.

$$x+1=\sqrt{6} x+1=-\sqrt{6}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\sqrt{6}-1 x=-\sqrt{6}-1$$