36x^2+2x-6=0 eching

$$36 x ^ { 2 } + 2 x - 6 = 0$$

x uchun yechish

$$x=\frac{\sqrt{217}-1}{36}\approx 0,381414441$$

$$x=\frac{-\sqrt{217}-1}{36}\approx -0,436969996$$

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.

$$36x^{2}+2x-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 36 ni a, 2 ni b va -6 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\times 36\left(-6\right)}}{2\times 36}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\times 36\left(-6\right)}}{2\times 36}$$

-4 ni 36 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-144\left(-6\right)}}{2\times 36}$$

-144 ni -6 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+864}}{2\times 36}$$

4 ni 864 ga qo'shish.

$$x=\frac{-2±\sqrt{868}}{2\times 36}$$

868 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{217}}{2\times 36}$$

2 ni 36 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{217}}{72}$$

x=\frac{-2±2\sqrt{217}}{72} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{217} ga qo'shish.

$$x=\frac{2\sqrt{217}-2}{72}$$

-2+2\sqrt{217} ni 72 ga bo'lish.

$$x=\frac{\sqrt{217}-1}{36}$$

x=\frac{-2±2\sqrt{217}}{72} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{217} ni ayirish.

$$x=\frac{-2\sqrt{217}-2}{72}$$

-2-2\sqrt{217} ni 72 ga bo'lish.

$$x=\frac{-\sqrt{217}-1}{36}$$

Tenglama yechildi.

$$x=\frac{\sqrt{217}-1}{36} x=\frac{-\sqrt{217}-1}{36}$$

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.

$$36x^{2}+2x-6=0$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$36x^{2}+2x-6-\left(-6\right)=-\left(-6\right)$$

O‘zidan -6 ayirilsa 0 qoladi.

$$36x^{2}+2x=-\left(-6\right)$$

0 dan -6 ni ayirish.

$$36x^{2}+2x=6$$

Ikki tarafini 36 ga bo‘ling.

$$\frac{36x^{2}+2x}{36}=\frac{6}{36}$$

36 ga bo'lish 36 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{2}{36}x=\frac{6}{36}$$

\frac{2}{36} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{18}x=\frac{6}{36}$$

\frac{6}{36} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{18}x=\frac{1}{6}$$

\frac{1}{18} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{36} olish uchun. Keyin, \frac{1}{36} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{18}x+\left(\frac{1}{36}\right)^{2}=\frac{1}{6}+\left(\frac{1}{36}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{36} kvadratini chiqarish.

$$x^{2}+\frac{1}{18}x+\frac{1}{1296}=\frac{1}{6}+\frac{1}{1296}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{6} ni \frac{1}{1296} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{1}{18}x+\frac{1}{1296}=\frac{217}{1296}$$

x^{2}+\frac{1}{18}x+\frac{1}{1296} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{36}\right)^{2}=\frac{217}{1296}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{36}\right)^{2}}=\sqrt{\frac{217}{1296}}$$

Qisqartirish.

$$x+\frac{1}{36}=\frac{\sqrt{217}}{36} x+\frac{1}{36}=-\frac{\sqrt{217}}{36}$$

Tenglamaning ikkala tarafidan \frac{1}{36} ni ayirish.

$$x=\frac{\sqrt{217}-1}{36} x=\frac{-\sqrt{217}-1}{36}$$