-x^2+10x-81=0 eching

$$- { x }^{ 2 } +10x-81=0$$

x uchun yechish (complex solution)

$$x=-2\sqrt{14}i+5\approx 5-7,483314774i$$

$$x=5+2\sqrt{14}i\approx 5+7,483314774i$$

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.

$$-x^{2}+10x-81=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 10 ni b va -81 ni c bilan almashtiring.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-1\right)\left(-81\right)}}{2\left(-1\right)}$$

10 kvadratini chiqarish.

$$x=\frac{-10±\sqrt{100-4\left(-1\right)\left(-81\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100+4\left(-81\right)}}{2\left(-1\right)}$$

4 ni -81 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100-324}}{2\left(-1\right)}$$

100 ni -324 ga qo'shish.

$$x=\frac{-10±\sqrt{-224}}{2\left(-1\right)}$$

-224 ning kvadrat ildizini chiqarish.

$$x=\frac{-10±4\sqrt{14}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-10±4\sqrt{14}i}{-2}$$

x=\frac{-10±4\sqrt{14}i}{-2} tenglamasini yeching, bunda ± musbat. -10 ni 4i\sqrt{14} ga qo'shish.

$$x=\frac{-10+4\sqrt{14}i}{-2}$$

-10+4i\sqrt{14} ni -2 ga bo'lish.

$$x=-2\sqrt{14}i+5$$

x=\frac{-10±4\sqrt{14}i}{-2} tenglamasini yeching, bunda ± manfiy. -10 dan 4i\sqrt{14} ni ayirish.

$$x=\frac{-4\sqrt{14}i-10}{-2}$$

-10-4i\sqrt{14} ni -2 ga bo'lish.

$$x=5+2\sqrt{14}i$$

Tenglama yechildi.

$$x=-2\sqrt{14}i+5 x=5+2\sqrt{14}i$$

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.

$$-x^{2}+10x-81=0$$

81 ni tenglamaning ikkala tarafiga qo'shish.

$$-x^{2}+10x-81-\left(-81\right)=-\left(-81\right)$$

O‘zidan -81 ayirilsa 0 qoladi.

$$-x^{2}+10x=-\left(-81\right)$$

0 dan -81 ni ayirish.

$$-x^{2}+10x=81$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+10x}{-1}=\frac{81}{-1}$$

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

$$x^{2}+\frac{10}{-1}x=\frac{81}{-1}$$

10 ni -1 ga bo'lish.

$$x^{2}-10x=\frac{81}{-1}$$

81 ni -1 ga bo'lish.

$$x^{2}-10x=-81$$

-10 ni bo‘lish, x shartining koeffitsienti, 2 ga -5 olish uchun. Keyin, -5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-10x+\left(-5\right)^{2}=-81+\left(-5\right)^{2}$$

-5 kvadratini chiqarish.

$$x^{2}-10x+25=-81+25$$

-81 ni 25 ga qo'shish.

$$x^{2}-10x+25=-56$$

x^{2}-10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-5\right)^{2}=-56$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{-56}$$

Qisqartirish.

$$x-5=2\sqrt{14}i x-5=-2\sqrt{14}i$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5+2\sqrt{14}i x=-2\sqrt{14}i+5$$