x^2+20x+100=-9 eching

$${ x }^{ 2 } +20x+100=-9$$

x uchun yechish (complex solution)

$$x=-10+3i$$

$$x=-10-3i$$

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.

$$x^{2}+20x+100=-9$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+20x+100-\left(-9\right)=-9-\left(-9\right)$$

O‘zidan -9 ayirilsa 0 qoladi.

$$x^{2}+20x+100-\left(-9\right)=0$$

100 dan -9 ni ayirish.

$$x^{2}+20x+109=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 20 ni b va 109 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\times 109}}{2}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\times 109}}{2}$$

-4 ni 109 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400-436}}{2}$$

400 ni -436 ga qo'shish.

$$x=\frac{-20±\sqrt{-36}}{2}$$

-36 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±6i}{2}$$

x=\frac{-20±6i}{2} tenglamasini yeching, bunda ± musbat. -20 ni 6i ga qo'shish.

$$x=\frac{-20+6i}{2}$$

-20+6i ni 2 ga bo'lish.

$$x=-10+3i$$

x=\frac{-20±6i}{2} tenglamasini yeching, bunda ± manfiy. -20 dan 6i ni ayirish.

$$x=\frac{-20-6i}{2}$$

-20-6i ni 2 ga bo'lish.

$$x=-10-3i$$

Tenglama yechildi.

$$x=-10+3i x=-10-3i$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2}+20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+10\right)^{2}=-9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{-9}$$

Qisqartirish.

$$x+10=3i x+10=-3i$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$x=-10+3i x=-10-3i$$