x^2+140x=261 eching

$$x ^ { 2 } + 140 x = 261$$

x uchun yechish (complex solution)

$$x=\sqrt{5161}-70\approx 1,840100223$$

$$x=-\left(\sqrt{5161}+70\right)\approx -141,840100223$$

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.

$$x^{2}+140x=261$$

Tenglamaning ikkala tarafidan 261 ni ayirish.

$$x^{2}+140x-261=261-261$$

O‘zidan 261 ayirilsa 0 qoladi.

$$x^{2}+140x-261=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 140 ni b va -261 ni c bilan almashtiring.

$$x=\frac{-140±\sqrt{140^{2}-4\left(-261\right)}}{2}$$

140 kvadratini chiqarish.

$$x=\frac{-140±\sqrt{19600-4\left(-261\right)}}{2}$$

-4 ni -261 marotabaga ko'paytirish.

$$x=\frac{-140±\sqrt{19600+1044}}{2}$$

19600 ni 1044 ga qo'shish.

$$x=\frac{-140±\sqrt{20644}}{2}$$

20644 ning kvadrat ildizini chiqarish.

$$x=\frac{-140±2\sqrt{5161}}{2}$$

x=\frac{-140±2\sqrt{5161}}{2} tenglamasini yeching, bunda ± musbat. -140 ni 2\sqrt{5161} ga qo'shish.

$$x=\frac{2\sqrt{5161}-140}{2}$$

-140+2\sqrt{5161} ni 2 ga bo'lish.

$$x=\sqrt{5161}-70$$

x=\frac{-140±2\sqrt{5161}}{2} tenglamasini yeching, bunda ± manfiy. -140 dan 2\sqrt{5161} ni ayirish.

$$x=\frac{-2\sqrt{5161}-140}{2}$$

-140-2\sqrt{5161} ni 2 ga bo'lish.

$$x=-\sqrt{5161}-70$$

Tenglama yechildi.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$

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.

$$x^{2}+140x=261$$

140 ni bo‘lish, x shartining koeffitsienti, 2 ga 70 olish uchun. Keyin, 70 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+140x+70^{2}=261+70^{2}$$

70 kvadratini chiqarish.

$$x^{2}+140x+4900=261+4900$$

261 ni 4900 ga qo'shish.

$$x^{2}+140x+4900=5161$$

x^{2}+140x+4900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+70\right)^{2}=5161$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+70\right)^{2}}=\sqrt{5161}$$

Qisqartirish.

$$x+70=\sqrt{5161} x+70=-\sqrt{5161}$$

Tenglamaning ikkala tarafidan 70 ni ayirish.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$

x uchun yechish

$$x=\sqrt{5161}-70\approx 1,840100223$$

$$x=-\sqrt{5161}-70\approx -141,840100223$$

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.

$$x^{2}+140x=261$$

Tenglamaning ikkala tarafidan 261 ni ayirish.

$$x^{2}+140x-261=261-261$$

O‘zidan 261 ayirilsa 0 qoladi.

$$x^{2}+140x-261=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 140 ni b va -261 ni c bilan almashtiring.

$$x=\frac{-140±\sqrt{140^{2}-4\left(-261\right)}}{2}$$

140 kvadratini chiqarish.

$$x=\frac{-140±\sqrt{19600-4\left(-261\right)}}{2}$$

-4 ni -261 marotabaga ko'paytirish.

$$x=\frac{-140±\sqrt{19600+1044}}{2}$$

19600 ni 1044 ga qo'shish.

$$x=\frac{-140±\sqrt{20644}}{2}$$

20644 ning kvadrat ildizini chiqarish.

$$x=\frac{-140±2\sqrt{5161}}{2}$$

x=\frac{-140±2\sqrt{5161}}{2} tenglamasini yeching, bunda ± musbat. -140 ni 2\sqrt{5161} ga qo'shish.

$$x=\frac{2\sqrt{5161}-140}{2}$$

-140+2\sqrt{5161} ni 2 ga bo'lish.

$$x=\sqrt{5161}-70$$

x=\frac{-140±2\sqrt{5161}}{2} tenglamasini yeching, bunda ± manfiy. -140 dan 2\sqrt{5161} ni ayirish.

$$x=\frac{-2\sqrt{5161}-140}{2}$$

-140-2\sqrt{5161} ni 2 ga bo'lish.

$$x=-\sqrt{5161}-70$$

Tenglama yechildi.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$

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.

$$x^{2}+140x=261$$

140 ni bo‘lish, x shartining koeffitsienti, 2 ga 70 olish uchun. Keyin, 70 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+140x+70^{2}=261+70^{2}$$

70 kvadratini chiqarish.

$$x^{2}+140x+4900=261+4900$$

261 ni 4900 ga qo'shish.

$$x^{2}+140x+4900=5161$$

x^{2}+140x+4900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+70\right)^{2}=5161$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+70\right)^{2}}=\sqrt{5161}$$

Qisqartirish.

$$x+70=\sqrt{5161} x+70=-\sqrt{5161}$$

Tenglamaning ikkala tarafidan 70 ni ayirish.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$