5x^2-70x+245=0 eching

$$5 x ^ { 2 } - 70 x + 245 = 0$$

x uchun yechish

$$x=7$$

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.

$$5x^{2}-70x+245=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -70 ni b va 245 ni c bilan almashtiring.

$$x=\frac{-\left(-70\right)±\sqrt{\left(-70\right)^{2}-4\times 5\times 245}}{2\times 5}$$

-70 kvadratini chiqarish.

$$x=\frac{-\left(-70\right)±\sqrt{4900-4\times 5\times 245}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-70\right)±\sqrt{4900-20\times 245}}{2\times 5}$$

-20 ni 245 marotabaga ko'paytirish.

$$x=\frac{-\left(-70\right)±\sqrt{4900-4900}}{2\times 5}$$

4900 ni -4900 ga qo'shish.

$$x=\frac{-\left(-70\right)±\sqrt{0}}{2\times 5}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{-70}{2\times 5}$$

-70 ning teskarisi 70 ga teng.

$$x=\frac{70}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{70}{10}$$

70 ni 10 ga bo'lish.

$$x=7$$

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.

$$5x^{2}-70x+245=0$$

Tenglamaning ikkala tarafidan 245 ni ayirish.

$$5x^{2}-70x+245-245=-245$$

O‘zidan 245 ayirilsa 0 qoladi.

$$5x^{2}-70x=-245$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-70x}{5}=-\frac{245}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{70}{5}\right)x=-\frac{245}{5}$$

-70 ni 5 ga bo'lish.

$$x^{2}-14x=-\frac{245}{5}$$

-245 ni 5 ga bo'lish.

$$x^{2}-14x=-49$$

-14 ni bo‘lish, x shartining koeffitsienti, 2 ga -7 olish uchun. Keyin, -7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-14x+\left(-7\right)^{2}=-49+\left(-7\right)^{2}$$

-7 kvadratini chiqarish.

$$x^{2}-14x+49=-49+49$$

-49 ni 49 ga qo'shish.

$$x^{2}-14x+49=0$$

x^{2}-14x+49 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-7\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-7\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x-7=0 x-7=0$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=7$$

Tenglama yechildi. Yechimlar bir xil.

$$x=7$$