-x^2+4x-29=0 eching

$$- x ^ { 2 } + 4 x - 29 = 0$$

x uchun yechish (complex solution)

$$x=2-5i$$

$$x=2+5i$$

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.

$$-x^{2}+4x-29=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 4 ni b va -29 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-29\right)}}{2\left(-1\right)}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-1\right)\left(-29\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+4\left(-29\right)}}{2\left(-1\right)}$$

4 ni -29 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-116}}{2\left(-1\right)}$$

16 ni -116 ga qo'shish.

$$x=\frac{-4±\sqrt{-100}}{2\left(-1\right)}$$

-100 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±10i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±10i}{-2}$$

x=\frac{-4±10i}{-2} tenglamasini yeching, bunda ± musbat. -4 ni 10i ga qo'shish.

$$x=\frac{-4+10i}{-2}$$

-4+10i ni -2 ga bo'lish.

$$x=2-5i$$

x=\frac{-4±10i}{-2} tenglamasini yeching, bunda ± manfiy. -4 dan 10i ni ayirish.

$$x=\frac{-4-10i}{-2}$$

-4-10i ni -2 ga bo'lish.

$$x=2+5i$$

Tenglama yechildi.

$$x=2-5i x=2+5i$$

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.

$$-x^{2}+4x-29=0$$

29 ni tenglamaning ikkala tarafiga qo'shish.

$$-x^{2}+4x-29-\left(-29\right)=-\left(-29\right)$$

O‘zidan -29 ayirilsa 0 qoladi.

$$-x^{2}+4x=-\left(-29\right)$$

0 dan -29 ni ayirish.

$$-x^{2}+4x=29$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+4x}{-1}=\frac{29}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{4}{-1}x=\frac{29}{-1}$$

4 ni -1 ga bo'lish.

$$x^{2}-4x=\frac{29}{-1}$$

29 ni -1 ga bo'lish.

$$x^{2}-4x=-29$$

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

$$x^{2}-4x+\left(-2\right)^{2}=-29+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=-29+4$$

-29 ni 4 ga qo'shish.

$$x^{2}-4x+4=-25$$

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

$$\left(x-2\right)^{2}=-25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{-25}$$

Qisqartirish.

$$x-2=5i x-2=-5i$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2+5i x=2-5i$$