8x=1-x^2 eching

$$8 x = 1 - x ^ { 2 }$$

x uchun yechish (complex solution)

$$x=\sqrt{17}-4\approx 0,123105626$$

$$x=-\left(\sqrt{17}+4\right)\approx -8,123105626$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1 ni ayirish.

$$8x-1=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$8x-1+x^{2}=0$$

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.

$$x^{2}+8x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 8 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-1\right)}}{2}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+4}}{2}$$

64 ni 4 ga qo'shish.

$$x=\frac{-8±\sqrt{68}}{2}$$

68 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{17}}{2}$$

x=\frac{-8±2\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{17} ga qo'shish.

$$x=\frac{2\sqrt{17}-8}{2}$$

-8+2\sqrt{17} ni 2 ga bo'lish.

$$x=\sqrt{17}-4$$

x=\frac{-8±2\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{17} ni ayirish.

$$x=\frac{-2\sqrt{17}-8}{2}$$

-8-2\sqrt{17} ni 2 ga bo'lish.

$$x=-\sqrt{17}-4$$

Tenglama yechildi.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} ni ikki tarafga qo’shing.

$$8x+x^{2}=1$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}+8x=1$$

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

$$x^{2}+8x+4^{2}=1+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=1+16$$

1 ni 16 ga qo'shish.

$$x^{2}+8x+16=17$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=17$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{17}$$

Qisqartirish.

$$x+4=\sqrt{17} x+4=-\sqrt{17}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$

x uchun yechish

$$x=\sqrt{17}-4\approx 0,123105626$$

$$x=-\sqrt{17}-4\approx -8,123105626$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 1 ni ayirish.

$$8x-1=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$8x-1+x^{2}=0$$

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.

$$x^{2}+8x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 8 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-1\right)}}{2}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+4}}{2}$$

64 ni 4 ga qo'shish.

$$x=\frac{-8±\sqrt{68}}{2}$$

68 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±2\sqrt{17}}{2}$$

x=\frac{-8±2\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{17} ga qo'shish.

$$x=\frac{2\sqrt{17}-8}{2}$$

-8+2\sqrt{17} ni 2 ga bo'lish.

$$x=\sqrt{17}-4$$

x=\frac{-8±2\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{17} ni ayirish.

$$x=\frac{-2\sqrt{17}-8}{2}$$

-8-2\sqrt{17} ni 2 ga bo'lish.

$$x=-\sqrt{17}-4$$

Tenglama yechildi.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} ni ikki tarafga qo’shing.

$$8x+x^{2}=1$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}+8x=1$$

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

$$x^{2}+8x+4^{2}=1+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=1+16$$

1 ni 16 ga qo'shish.

$$x^{2}+8x+16=17$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=17$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{17}$$

Qisqartirish.

$$x+4=\sqrt{17} x+4=-\sqrt{17}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$