x^2-25x+104=-7x-3 eching

$$x ^ { 2 } - 25 x + 104 = - 7 x - 3$$

x uchun yechish (complex solution)

$$x=9+\sqrt{26}i\approx 9+5,099019514i$$

$$x=-\sqrt{26}i+9\approx 9-5,099019514i$$

Kvadrat tenglamalaridan foydalanish qoidalari

7x ni ikki tarafga qo’shing.

$$x^{2}-25x+104+7x=-3$$

-18x ni olish uchun -25x va 7x ni birlashtirish.

$$x^{2}-18x+104=-3$$

3 ni ikki tarafga qo’shing.

$$x^{2}-18x+104+3=0$$

107 olish uchun 104 va 3'ni qo'shing.

$$x^{2}-18x+107=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -18 ni b va 107 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 107}}{2}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 107}}{2}$$

-4 ni 107 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-428}}{2}$$

324 ni -428 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{-104}}{2}$$

-104 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±2\sqrt{26}i}{2}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±2\sqrt{26}i}{2}$$

x=\frac{18±2\sqrt{26}i}{2} tenglamasini yeching, bunda ± musbat. 18 ni 2i\sqrt{26} ga qo'shish.

$$x=\frac{18+2\sqrt{26}i}{2}$$

18+2i\sqrt{26} ni 2 ga bo'lish.

$$x=9+\sqrt{26}i$$

x=\frac{18±2\sqrt{26}i}{2} tenglamasini yeching, bunda ± manfiy. 18 dan 2i\sqrt{26} ni ayirish.

$$x=\frac{-2\sqrt{26}i+18}{2}$$

18-2i\sqrt{26} ni 2 ga bo'lish.

$$x=-\sqrt{26}i+9$$

Tenglama yechildi.

$$x=9+\sqrt{26}i x=-\sqrt{26}i+9$$

Kvadratni yakunlash bo'yicha qadamlar

7x ni ikki tarafga qo’shing.

$$x^{2}-25x+104+7x=-3$$

-18x ni olish uchun -25x va 7x ni birlashtirish.

$$x^{2}-18x+104=-3$$

Ikkala tarafdan 104 ni ayirish.

$$x^{2}-18x=-3-104$$

-107 olish uchun -3 dan 104 ni ayirish.

$$x^{2}-18x=-107$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-18x+\left(-9\right)^{2}=-107+\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$x^{2}-18x+81=-107+81$$

-107 ni 81 ga qo'shish.

$$x^{2}-18x+81=-26$$

x^{2}-18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-9\right)^{2}=-26$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{-26}$$

Qisqartirish.

$$x-9=\sqrt{26}i x-9=-\sqrt{26}i$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x=9+\sqrt{26}i x=-\sqrt{26}i+9$$