x^2+10x+7=0 eching

$$x ^ { 2 } + 10 x + 7 = 0$$

x uchun yechish

$$x=3\sqrt{2}-5\approx -0,757359313$$

$$x=-3\sqrt{2}-5\approx -9,242640687$$

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.

$$x^{2}+10x+7=0$$

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 7 ni c bilan almashtiring.

$$x=\frac{-10±\sqrt{10^{2}-4\times 7}}{2}$$

10 kvadratini chiqarish.

$$x=\frac{-10±\sqrt{100-4\times 7}}{2}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100-28}}{2}$$

100 ni -28 ga qo'shish.

$$x=\frac{-10±\sqrt{72}}{2}$$

72 ning kvadrat ildizini chiqarish.

$$x=\frac{-10±6\sqrt{2}}{2}$$

x=\frac{-10±6\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. -10 ni 6\sqrt{2} ga qo'shish.

$$x=\frac{6\sqrt{2}-10}{2}$$

-10+6\sqrt{2} ni 2 ga bo'lish.

$$x=3\sqrt{2}-5$$

x=\frac{-10±6\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. -10 dan 6\sqrt{2} ni ayirish.

$$x=\frac{-6\sqrt{2}-10}{2}$$

-10-6\sqrt{2} ni 2 ga bo'lish.

$$x=-3\sqrt{2}-5$$

Tenglama yechildi.

$$x=3\sqrt{2}-5 x=-3\sqrt{2}-5$$

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.

$$x^{2}+10x+7=0$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x^{2}+10x+7-7=-7$$

O‘zidan 7 ayirilsa 0 qoladi.

$$x^{2}+10x=-7$$

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.

$$x^{2}+10x+5^{2}=-7+5^{2}$$

5 kvadratini chiqarish.

$$x^{2}+10x+25=-7+25$$

-7 ni 25 ga qo'shish.

$$x^{2}+10x+25=18$$

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.

$$\left(x+5\right)^{2}=18$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{18}$$

Qisqartirish.

$$x+5=3\sqrt{2} x+5=-3\sqrt{2}$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$x=3\sqrt{2}-5 x=-3\sqrt{2}-5$$