x^2+100x+2500=0 eching

$$x ^ { 2 } + 100 x + 2500 = 0$$

x uchun yechish

$$x=-50$$

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.

$$x^{2}+100x+2500=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 100 ni b va 2500 ni c bilan almashtiring.

$$x=\frac{-100±\sqrt{100^{2}-4\times 2500}}{2}$$

100 kvadratini chiqarish.

$$x=\frac{-100±\sqrt{10000-4\times 2500}}{2}$$

-4 ni 2500 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000-10000}}{2}$$

10000 ni -10000 ga qo'shish.

$$x=\frac{-100±\sqrt{0}}{2}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{100}{2}$$

-100 ni 2 ga bo'lish.

$$x=-50$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2}+100x+2500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+50\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+50\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x+50=0 x+50=0$$

Tenglamaning ikkala tarafidan 50 ni ayirish.

$$x=-50 x=-50$$

Tenglama yechildi. Yechimlar bir xil.

$$x=-50$$