x^2+14x-38=0 eching

$${ x }^{ 2 } +14x-38=0$$

x uchun yechish (complex solution)

$$x=\sqrt{87}-7\approx 2,327379053$$

$$x=-\left(\sqrt{87}+7\right)\approx -16,327379053$$

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.

$$x^{2}+14x-38=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 14 ni b va -38 ni c bilan almashtiring.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-38\right)}}{2}$$

14 kvadratini chiqarish.

$$x=\frac{-14±\sqrt{196-4\left(-38\right)}}{2}$$

-4 ni -38 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+152}}{2}$$

196 ni 152 ga qo'shish.

$$x=\frac{-14±\sqrt{348}}{2}$$

348 ning kvadrat ildizini chiqarish.

$$x=\frac{-14±2\sqrt{87}}{2}$$

x=\frac{-14±2\sqrt{87}}{2} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{87} ga qo'shish.

$$x=\frac{2\sqrt{87}-14}{2}$$

-14+2\sqrt{87} ni 2 ga bo'lish.

$$x=\sqrt{87}-7$$

x=\frac{-14±2\sqrt{87}}{2} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{87} ni ayirish.

$$x=\frac{-2\sqrt{87}-14}{2}$$

-14-2\sqrt{87} ni 2 ga bo'lish.

$$x=-\sqrt{87}-7$$

Tenglama yechildi.

$$x=\sqrt{87}-7 x=-\sqrt{87}-7$$

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.

$$x^{2}+14x-38=0$$

38 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+14x-38-\left(-38\right)=-\left(-38\right)$$

O‘zidan -38 ayirilsa 0 qoladi.

$$x^{2}+14x=-\left(-38\right)$$

0 dan -38 ni ayirish.

$$x^{2}+14x=38$$

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.

$$x^{2}+14x+7^{2}=38+7^{2}$$

7 kvadratini chiqarish.

$$x^{2}+14x+49=38+49$$

38 ni 49 ga qo'shish.

$$x^{2}+14x+49=87$$

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.

$$\left(x+7\right)^{2}=87$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+7\right)^{2}}=\sqrt{87}$$

Qisqartirish.

$$x+7=\sqrt{87} x+7=-\sqrt{87}$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x=\sqrt{87}-7 x=-\sqrt{87}-7$$

x uchun yechish

$$x=\sqrt{87}-7\approx 2,327379053$$

$$x=-\sqrt{87}-7\approx -16,327379053$$

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.

$$x^{2}+14x-38=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 14 ni b va -38 ni c bilan almashtiring.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-38\right)}}{2}$$

14 kvadratini chiqarish.

$$x=\frac{-14±\sqrt{196-4\left(-38\right)}}{2}$$

-4 ni -38 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+152}}{2}$$

196 ni 152 ga qo'shish.

$$x=\frac{-14±\sqrt{348}}{2}$$

348 ning kvadrat ildizini chiqarish.

$$x=\frac{-14±2\sqrt{87}}{2}$$

x=\frac{-14±2\sqrt{87}}{2} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{87} ga qo'shish.

$$x=\frac{2\sqrt{87}-14}{2}$$

-14+2\sqrt{87} ni 2 ga bo'lish.

$$x=\sqrt{87}-7$$

x=\frac{-14±2\sqrt{87}}{2} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{87} ni ayirish.

$$x=\frac{-2\sqrt{87}-14}{2}$$

-14-2\sqrt{87} ni 2 ga bo'lish.

$$x=-\sqrt{87}-7$$

Tenglama yechildi.

$$x=\sqrt{87}-7 x=-\sqrt{87}-7$$

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.

$$x^{2}+14x-38=0$$

38 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+14x-38-\left(-38\right)=-\left(-38\right)$$

O‘zidan -38 ayirilsa 0 qoladi.

$$x^{2}+14x=-\left(-38\right)$$

0 dan -38 ni ayirish.

$$x^{2}+14x=38$$

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.

$$x^{2}+14x+7^{2}=38+7^{2}$$

7 kvadratini chiqarish.

$$x^{2}+14x+49=38+49$$

38 ni 49 ga qo'shish.

$$x^{2}+14x+49=87$$

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.

$$\left(x+7\right)^{2}=87$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+7\right)^{2}}=\sqrt{87}$$

Qisqartirish.

$$x+7=\sqrt{87} x+7=-\sqrt{87}$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x=\sqrt{87}-7 x=-\sqrt{87}-7$$